{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Untitled2.ipynb",
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/letianzj/QuantResearch/blob/master/notebooks/arima_garch.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "VOE2BiQb4zHd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "e93c28d5-0478-42c3-9abe-ccdf9faf4f86"
      },
      "source": [
        "%matplotlib inline\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import scipy\n",
        "from datetime import datetime, timedelta\n",
        "import statsmodels.api as sm\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas_datareader as pdr"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d6lqkX0A-ihT",
        "colab_type": "text"
      },
      "source": [
        "### Download Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "f-a_lphzrH4C",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 187
        },
        "outputId": "26c6b33d-90b2-4dff-c324-5bfcd5fef9da"
      },
      "source": [
        "end_date = datetime.today()\n",
        "# start_date = end_date + timedelta(days=-5*365)\n",
        "start_date = datetime(2000, 1, 1)\n",
        "spx = pdr.DataReader(name='^GSPC', data_source='yahoo', start=start_date, end=end_date)\n",
        "hist_close = spx['Close']\n",
        "hist_ret = hist_close / hist_close.shift(1) - 1.0     # shift 1 shifts forward one day; today has yesterday's price\n",
        "# hist_ret = hist_close.pct_change(1)\n",
        "hist_ret.dropna(inplace=True)\n",
        "hist_ret = hist_ret * 100.0\n",
        "print(hist_ret.describe())\n",
        "print(f'Skew: {scipy.stats.skew(hist_ret)}, Kurtosis: {scipy.stats.kurtosis(hist_ret)}')"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "count    5155.000000\n",
            "mean        0.022599\n",
            "std         1.257874\n",
            "min       -11.984055\n",
            "25%        -0.478822\n",
            "50%         0.056389\n",
            "75%         0.573434\n",
            "max        11.580037\n",
            "Name: Close, dtype: float64\n",
            "Skew: -0.14209031793258495, Kurtosis: 10.805446588849396\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rxStiN6h-ihX",
        "colab_type": "text"
      },
      "source": [
        "### ARIMA Model\n",
        "#### Step One: Identify (p, d, q)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z0onSzin-ihY",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "0b7936bf-7387-4110-dcf8-6e0b3f324943"
      },
      "source": [
        "# price is known to be non-stationary; return is stationary\n",
        "from statsmodels.tsa.stattools import adfuller\n",
        "\n",
        "result = adfuller(hist_close)\n",
        "print(f'ADF Statistic: {result[0]}, p-value: {result[1]}')  # null hypothesis: unit root exists; can't reject null.\n",
        "\n",
        "result = adfuller(hist_ret)\n",
        "print(f'ADF Statistic: {result[0]}, p-value: {result[1]}')   # reject null hypothesis of unit root ==> stationary          "
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ADF Statistic: 0.5193392311354961, p-value: 0.985449193626401\n",
            "ADF Statistic: -13.668804657981337, p-value: 1.473122279668348e-25\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7RkF9lo7-iha",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 383
        },
        "outputId": "d300fb75-6cec-490c-a3c4-e3419ddce422"
      },
      "source": [
        "from statsmodels.tsa.stattools import acf, pacf\n",
        "from statsmodels.graphics.tsaplots import plot_acf, plot_pacf\n",
        "\n",
        "fig, axes = plt.subplots(1, 2, sharex=True, figsize=(16, 4))\n",
        "plot_acf(hist_ret, ax=axes[0])          # determines MA(q)\n",
        "plot_pacf(hist_ret, ax=axes[1])         # determines AR(p)\n",
        "plt.show()\n",
        "\n",
        "act_stats = acf(hist_ret, fft=False)[1:40]                \n",
        "acf_df = pd.DataFrame([act_stats]).T\n",
        "acf_df.columns = ['acf']\n",
        "acf_df.index += 1\n",
        "\n",
        "pacf_stats = pacf(hist_ret)[1:40]                        \n",
        "pacf_df = pd.DataFrame([pacf_stats]).T\n",
        "pacf_df.columns = ['pacf']\n",
        "pacf_df.index += 1\n",
        "\n",
        "df_acf_pcaf = pd.concat([acf_df, pacf_df], axis=1)\n",
        "print(df_acf_pcaf.head())"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1152x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "        acf      pacf\n",
            "1 -0.115067 -0.115089\n",
            "2 -0.011660 -0.025245\n",
            "3  0.015008  0.010886\n",
            "4 -0.029457 -0.027119\n",
            "5 -0.014346 -0.020789\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2a47oEb6-ihd",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "8e2624f8-895a-452c-eb44-1bf4d0c6b5b5"
      },
      "source": [
        "# acf/pacf suggests higher order of arounds 35 business days; which makes the model practically unusable.\n",
        "# instead, let's constraint the order to 5 business days and use AIC to pick up the best fit\n",
        "from statsmodels.tsa.arima_model import ARIMA, ARMA\n",
        "\n",
        "hist_training = hist_ret.iloc[:-45]\n",
        "hist_testing = hist_ret.iloc[-45:]\n",
        "\n",
        "dict_aic = {}\n",
        "for p in range(6):\n",
        "    for q in range(6):\n",
        "        try:\n",
        "            model = ARIMA(hist_training, order=(p, 0, q))\n",
        "            model_fit = model.fit(disp=0)\n",
        "            dict_aic[(p, q)] = model_fit.aic\n",
        "        except:\n",
        "            pass\n",
        "df_aic = pd.DataFrame.from_dict(dict_aic, orient='index', columns=['aic'])\n",
        "p, q = df_aic[df_aic.aic == df_aic.aic.min()].index[0]\n",
        "print(f'ARIMA order is ({p}, {0}, {q})')"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "ARIMA order is (5, 0, 5)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vn2k0eJb-ihh",
        "colab_type": "text"
      },
      "source": [
        "#### Step Two: Fit the Model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zXlkqNpe-ihh",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 704
        },
        "outputId": "8bd7ea00-dc71-4979-e751-d2fa5d94f3f1"
      },
      "source": [
        "# train the selected model\n",
        "model = ARIMA(hist_training, order=(p, 0, q))\n",
        "arima_fitted = model.fit(disp=0)\n",
        "arima_fitted.summary()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
            "  ' ignored when e.g. forecasting.', ValueWarning)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>       <td>Close</td>      <th>  No. Observations:  </th>   <td>5110</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(5, 5)</td>    <th>  Log Likelihood     </th> <td>-8347.672</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.239</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Wed, 01 Jul 2020</td> <th>  AIC                </th> <td>16719.343</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>01:33:56</td>     <th>  BIC                </th> <td>16797.811</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>                <td>0</td>        <th>  HQIC               </th> <td>16746.815</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                       <td> </td>        <th>                     </th>     <td> </td>    \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "       <td></td>          <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th>       <td>    0.0212</td> <td>    0.014</td> <td>    1.471</td> <td> 0.141</td> <td>   -0.007</td> <td>    0.049</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.Close</th> <td>   -0.8244</td> <td>    0.140</td> <td>   -5.874</td> <td> 0.000</td> <td>   -1.100</td> <td>   -0.549</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L2.Close</th> <td>   -0.3461</td> <td>    0.184</td> <td>   -1.884</td> <td> 0.060</td> <td>   -0.706</td> <td>    0.014</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L3.Close</th> <td>   -0.5808</td> <td>    0.171</td> <td>   -3.400</td> <td> 0.001</td> <td>   -0.916</td> <td>   -0.246</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L4.Close</th> <td>   -0.1537</td> <td>    0.179</td> <td>   -0.857</td> <td> 0.392</td> <td>   -0.505</td> <td>    0.198</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L5.Close</th> <td>    0.4618</td> <td>    0.107</td> <td>    4.302</td> <td> 0.000</td> <td>    0.251</td> <td>    0.672</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.Close</th> <td>    0.7109</td> <td>    0.136</td> <td>    5.212</td> <td> 0.000</td> <td>    0.444</td> <td>    0.978</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L2.Close</th> <td>    0.2398</td> <td>    0.166</td> <td>    1.440</td> <td> 0.150</td> <td>   -0.087</td> <td>    0.566</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L3.Close</th> <td>    0.5423</td> <td>    0.152</td> <td>    3.566</td> <td> 0.000</td> <td>    0.244</td> <td>    0.840</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L4.Close</th> <td>    0.0584</td> <td>    0.165</td> <td>    0.354</td> <td> 0.723</td> <td>   -0.265</td> <td>    0.381</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L5.Close</th> <td>   -0.5215</td> <td>    0.097</td> <td>   -5.391</td> <td> 0.000</td> <td>   -0.711</td> <td>   -0.332</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>          -0.9516</td> <td>          -0.4066j</td> <td>           1.0348</td> <td>          -0.4357</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.2</th> <td>          -0.9516</td> <td>          +0.4066j</td> <td>           1.0348</td> <td>           0.4357</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.3</th> <td>           0.2227</td> <td>          -1.0391j</td> <td>           1.0627</td> <td>          -0.2164</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.4</th> <td>           0.2227</td> <td>          +1.0391j</td> <td>           1.0627</td> <td>           0.2164</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.5</th> <td>           1.7906</td> <td>          -0.0000j</td> <td>           1.7906</td> <td>          -0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>          -0.9683</td> <td>          -0.4039j</td> <td>           1.0492</td> <td>          -0.4371</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.2</th> <td>          -0.9683</td> <td>          +0.4039j</td> <td>           1.0492</td> <td>           0.4371</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.3</th> <td>           0.2298</td> <td>          -1.0216j</td> <td>           1.0471</td> <td>          -0.2148</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.4</th> <td>           0.2298</td> <td>          +1.0216j</td> <td>           1.0471</td> <td>           0.2148</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.5</th> <td>           1.5891</td> <td>          -0.0000j</td> <td>           1.5891</td> <td>          -0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:                  Close   No. Observations:                 5110\n",
              "Model:                     ARMA(5, 5)   Log Likelihood               -8347.672\n",
              "Method:                       css-mle   S.D. of innovations              1.239\n",
              "Date:                Wed, 01 Jul 2020   AIC                          16719.343\n",
              "Time:                        01:33:56   BIC                          16797.811\n",
              "Sample:                             0   HQIC                         16746.815\n",
              "                                                                              \n",
              "===============================================================================\n",
              "                  coef    std err          z      P>|z|      [0.025      0.975]\n",
              "-------------------------------------------------------------------------------\n",
              "const           0.0212      0.014      1.471      0.141      -0.007       0.049\n",
              "ar.L1.Close    -0.8244      0.140     -5.874      0.000      -1.100      -0.549\n",
              "ar.L2.Close    -0.3461      0.184     -1.884      0.060      -0.706       0.014\n",
              "ar.L3.Close    -0.5808      0.171     -3.400      0.001      -0.916      -0.246\n",
              "ar.L4.Close    -0.1537      0.179     -0.857      0.392      -0.505       0.198\n",
              "ar.L5.Close     0.4618      0.107      4.302      0.000       0.251       0.672\n",
              "ma.L1.Close     0.7109      0.136      5.212      0.000       0.444       0.978\n",
              "ma.L2.Close     0.2398      0.166      1.440      0.150      -0.087       0.566\n",
              "ma.L3.Close     0.5423      0.152      3.566      0.000       0.244       0.840\n",
              "ma.L4.Close     0.0584      0.165      0.354      0.723      -0.265       0.381\n",
              "ma.L5.Close    -0.5215      0.097     -5.391      0.000      -0.711      -0.332\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1           -0.9516           -0.4066j            1.0348           -0.4357\n",
              "AR.2           -0.9516           +0.4066j            1.0348            0.4357\n",
              "AR.3            0.2227           -1.0391j            1.0627           -0.2164\n",
              "AR.4            0.2227           +1.0391j            1.0627            0.2164\n",
              "AR.5            1.7906           -0.0000j            1.7906           -0.0000\n",
              "MA.1           -0.9683           -0.4039j            1.0492           -0.4371\n",
              "MA.2           -0.9683           +0.4039j            1.0492            0.4371\n",
              "MA.3            0.2298           -1.0216j            1.0471           -0.2148\n",
              "MA.4            0.2298           +1.0216j            1.0471            0.2148\n",
              "MA.5            1.5891           -0.0000j            1.5891           -0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FKTswv-a-ihl",
        "colab_type": "text"
      },
      "source": [
        "#### Step Three: Residual Analysis"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1wwM_8mf-ihl",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 363
        },
        "outputId": "46fc9e2a-32d6-4905-8e56-98ec31d0ecc3"
      },
      "source": [
        "# unfortunately it doesn't look like Gaussian;\n",
        "# which is somewhat expected, as acf/pacf graph has lags up to 2month ago.\n",
        "residuals = pd.DataFrame(arima_fitted.resid, columns=['residual'])\n",
        "fig, ax = plt.subplots(1,2, figsize=(10, 4))\n",
        "# residuals.plot(title=\"Residuals\", ax=ax[0])\n",
        "residuals.plot(kind='kde', title='Density', ax=ax[0])\n",
        "sm.qqplot(residuals, line='s', ax=ax[1])\n",
        "plt.show()\n",
        "\n",
        "# normality test\n",
        "from scipy.stats import shapiro, normaltest\n",
        "stat, p = normaltest(residuals)\n",
        "print(f'Statistics={stat[0]:.3f}, p={p[0]:.3f}')       # H0: Gaussian\n",
        "stat, p = shapiro(residuals)\n",
        "print(f'Statistics={stat:.3f}, p={p:.3f}')       # H0: Gaussian"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Statistics=993.870, p=0.000\n",
            "Statistics=0.895, p=0.000\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/scipy/stats/morestats.py:1676: UserWarning: p-value may not be accurate for N > 5000.\n",
            "  warnings.warn(\"p-value may not be accurate for N > 5000.\")\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fPGPoOHN-iho",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "27d4b007-abee-4012-dcbb-868e424f97f0"
      },
      "source": [
        "# Because we limit the lag orders; there still has remaining autocorrelation.\n",
        "fig, axes = plt.subplots(1, 2, figsize=(16, 4))\n",
        "plot_acf(residuals, ax=axes[0])\n",
        "plot_pacf(residuals, ax=axes[1])\n",
        "plt.show()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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J0hQzN0uS+kFTNzWSJEmSJKkjFqSSJEmSpCIsSCVJkiRJRViQSpIkSZKKsCCVJEmSJBVhQSpJkiRJKsKCVJIkSZJUhAWpJEmSJKkIC1JJkiRJUhEWpJIkSZKkIixIJUmSJElFWJBKkiRJkoqwIJUkSZIkFWFBKkmSJEkqwoJUkiRJklSEBakkSZIkqQgLUkmSJElSERakkiRJkqQiLEglSZIkSUVYkEqSJEmSirAglSRJkiQVYUEqSZIkSSrCglSSJEmSVIQFqSRJkiSpCAtSSZIkSVIRFqSSJEmSpCIsSCVJkiRJRViQSpIkSZKKqFWQRsQFEbExIjZFxLsnaPdfIiIjYlVzIUqSJEmS+tGkBWlEDAAfBS4EVgCXRsSKcdodBfwCcHvTQUqSpH05WSxJ6gd1zpCeA2zKzAcycwj4FHDxOO3+B/C7wLMNxidJksZwsliS1C/qFKRLgM1tj7dUy54XEWcDyzLzHyfqKCIuj4i1EbF2+/btHQcrSZIAJ4slSX3ikG9qFBGzgN8H3jVZ28y8OjNXZeaqhQsXHurQkiTNVE4WS5L6Qp2C9GFgWdvjpdWyUUcBLwVujYgHgZcDa/yuiiRJZThZLEnqFXUK0juA5RFxckQMApcAa0Z/mZnfyswFmXlSZp4EfAm4KDPXTknEkiTJyWJJUl+YtCDNzL3AFcBNwL3ADZm5PiKuioiLpjpASZK0HyeLJUl9YXadRpl5I3DjmGVXHqDt6kMPS5IkHUhm7o2I0cniAeCa0cliYG1mrpm4B0mSukOtglSSJHUXJ4slSf3gkO+yK0mSJEnSwbAglSRJkiQVYUEqSZIkSSrCglSSJEmSVIQFqSRJkiSpCAtSSZIkSVIRFqSSJEmSpCIsSCVJkiRJRViQSpIkSZKKsCCVJEmSJBVhQSpJkiRJKsKCVJIkSZJUhAWpJEmSJKkIC1JJkiRJUhEWpJIkSZKkIixIJUmSJElFWJBKkiRJkoqwIJUkSZIkFWFBKkmSJEkqwoJUkiRJklSEBakkSZIkqQgLUkmSJElSERakkiRJkqQiLEglSZIkSUVYkEqSJEmSirAglSRJkiQVYUEqSZIkSSrCglSSJEmSVEStgjQiLoiIjRGxKSLePc7vfykiNkTE3RFxc0Sc2HyokiRplLlZktQPJi1II2IA+ChwIbACuDQiVoxpdhewKjO/E/g08L+aDlSSJLWYmyVJ/aLOGdJzgE2Z+UBmDgGfAi5ub5CZt2TmM9XDLwFLmw1TkiS1MTdLkvpCnYJ0CbC57fGWatmBXAb803i/iIjLI2JtRKzdvn17/SglSVI7c7MkqS80elOjiPhpYBXwe+P9PjOvzsxVmblq4cKFTQ4tSZLGYW6WJHWz2TXaPAwsa3u8tFq2j4j4QeDXge/PzD3NhCdJksZhbpYk9YU6Z0jvAJZHxMkRMQhcAqxpbxARZwF/ClyUmduaD1OSJLUxN0uS+sKkBWlm7gWuAG4C7gVuyMz1EXFVRFxUNfs9YB7wNxGxLiLWHKA7SZJ0iMzNkqR+UeeSXTLzRuDGMcuubPv5BxuOS5IkTcDcLEnqB43e1EiSJEmSpLosSCVJkiRJRViQSpIkSZKKsCCVJEmSJBVhQSpJkiRJKsKCVJIkSZJUhAWpJEmSJKkIC1JJkiRJUhEWpJIkSZKkIixIJUmSJElFWJBKkiRJkoqwIJUkSZIkFWFBKkmSJEkqwoJUkiRJklSEBakkSZIkqQgLUkmSJElSERakkiRJkqQiLEglSZIkSUVYkEqSJEmSiphdOgCpmw2PJLdu3Mb6R3bxksVHs/r0RQzMitJhSZIkSX3BglQ6gOGR5I0fu511m3eye2iYuYMDrFw2n+suO9eiVJKkQpwslvqLBal0ALdu3Ma6zTt5ZmgYgGeGhlm3eSe3btzG+WccXzg6SZJmHieLpf7jd0ilA1j/yC52V8XoqN1Dw2x4ZFehiCRJmtnaJ4uTfSeL1T2GR5Kb793Kh2++n5vv3crwSJYOSV3MM6TaT51LYWbC5TIvWXw0cwcHnj9DCjB3cIAVi48uGJXGmgnboiTVMRP2hxNNFnv1UnfwLLY6ZUGqfdTZiUzFjqYbk+jq0xexctl8brvvUXLWbI6Ycxgrl81n9emLisalbzPpSZopJsuTM2V/6GRx9/MrT+pU3xakmV4acDBu+c+t4+5EbvnPrc/vROq06WT1D48kb/74f+yXRD/x1nOKJtEAPvHWc3jF63+GoSMX8Xu//k5Wn7aIqGKeCm634zvQWvn8f46f9D5371Ze9R1OHLTrdNMaHkm+cN92Njy6ixUnHM33nbZwSj6PA7Oirw6WpalQp9hsugjoxolicLK4F3gWW53qy4J042NP8s2nh0qH0ZNuWr913J3ITeu3cuScw2q36cSXH3qCOx96gj17R4BWEr3zoSe4+gsPcPaJLzjIV9KcvY9uZBYbmTfnV1j70BOlw1Gbz20Yf1v83IatHH1459viyEiybvNOHnz8aU467khWLpvPrC44AJtuIyPJb//TvWza9hRDe0cYnD2LUxfN470XntH4+jjxuCNYPH9uo31K/aZOsdlkEdDNZ1sHZgXXXXYu5/34ZQwduYgPvu8Xu6ZYVotnsdWpvixIp0qJg9XpHvOk445kcPas54tDgMHZszjpuCM7atOJBx9/mqG2vgCG9o7w4ONPd0VB2o2a3C6a3samc5ttclucziKs263bvJNN2556fr3u2TvCpm1PsW7zTj+TOmi3fe3xKel3Jkwkffarj41bbH72q49xxGDrUG4gYtz94ayIjtf9gSaK/+TWr3XNPmB0sviIwV/hP77+zdLhdLXp/owcPnuAkxccyfpv7ICB2cw5bDYnLziSw2cPHNR+YCZ8xuuarnVx3inHNd7nRGoVpBFxAfCHwADw55n5P8f8fg7wF8B3AY8Db8jMB5sN9eDUfeMma9fJwWpTG0uJA+SVy+Zz6qJ5++xETl00j5XL5nfUphN1iwp3SC1NbhdNb2PTvc02uS12UoR184RAE2NOxSSRn19NhRK5uem+6qiTJ5vcHzpRfHC6cRsrcSw5a1bw3gvP4Od+4V0MzzueK952+bTE3+95pp8nzictSCNiAPgo8GpgC3BHRKzJzA1tzS4DnsjMUyPiEuB3gTdMRcCdqPvG1WlX92C1yY2lxFmKOjuRJnc0UC+JdvOHcLrPMDa5XTRdhE33Ntvktlj3AKybJwSaGrPpqyAmGlMHz8niMrm5WyeLm9wfdrIP6NYiYLrj6tZtrNQVL7NmBYOPb4LHN3H2ib920P2U+IyXMp3Hf3XHnC51zpCeA2zKzAcAIuJTwMVAe0F6MfCB6udPAx+JiMgJ7tDywPanecOf3nZQQbd7dEWr7m3va/fQMM+NjPDks3t5eOfu52/msWfvCBse3cWv/d3dHHX4t196nXbbn9yzz455tN21/+/rfOaeRzrqC1o3r3lqzzDPPjfM4YcNMG/OABH7bgB1x5wKzy47F4DP3PPIAceq06bO6xxtN+vZnTAwyMJjT2B4ZITfvPHbm1jd9ToVdq38KQCu+sz6ceP+xjd3s/u5YTIhAuYeNsCLjp077uucTJ3+mtwu6vZV93V20l+d7aKuJrbFJ5/d27qTVfteK+C2Bx7nq498a592dbfFOmM21VdddcbMzNb3sXIECKK68dA/3P3wfuu3TlwTjblw3hwGZ/snsTvlZHGrXd2JpFITeU2pW2w2VQTUPdvarUXAVMTVq5PFvX62eyo+43WKsG6c0Ojkvaz7Grtlsjgmu6tnRLweuCAzf6Z6/Ebg3My8oq3NV6s2W6rHX6va7BjT1+XA5QDzTjjlu17z/uuafC3PGy1Itz+5hx1P7X9zo4XzBllw1JznH9dpN/aACloH5Uvmz93nwLFOX6MH98/seY7Rg73xDu7rjjna532bHoCBQRYvPuGAB6v3b/gqAMtXvHS/3zWt7uuso+57OTrudK2LTt6jOmPW6a/JMev21WS7TraLuu/lZOqM2UnRXWdbrDNmk32Nmmwb62TMp/YMs+e5YeYcoNCsG9dEYy59wRGNFaQ3vO177szMVY101uUi4jzgA5n5w9Xj9wBk5u+0tbmpanNbRMwGHgMWTjRZfOyJZ+Sr33vNIce37ivrAFh55srnl+169jmg2f1Jk7kZ6k8W181HTauTt+q0qfM66+x/O81HTWoit9VVd7K4qe2i09wwUVydHks2OVncxLY4FZ/xydZZJycbpmqyeLzXWXdd1I1/ov6WNHizwTq5eVpvapSZVwNXA6xatSr/+ufOm5JxRu+y++WHnuDDn79/nzM2c2bP4i3fc/I+Mwl12tWdbavT12gbonUQltm6o91rv3PJQV1+MNpu5PD5MDCb7U/u4Zi547f7uZs+xvC84/nRl/3QlM/21H2dnfQ12XtZd10AvP2T7wHgyl9dc7Avkb/78hY+feeWfRcmnPfi4/jxs5fu136yMev01+nM70Rj1u2r7uus01+n23+d93IynYw52Yxip/uVicZssq9Rk21jdceso25cE435Y2cvaewuuze8rZFuesUSYHPb4y3AuQdqk5l7I+JbwHHARJPFjQTXXoiO9Wx1kNQuE/Y8N7zPQVWddvPmDDD3sIH9DrzmzRnY53mHHzZABPsdeM05bKCt73oTLHX6au9zsqKuk4m3OhOok7Wp+zojgtOXT7w91H0vR8dtcrJ4ot93EledMZ/aM/z8Njba1+7nhnlqz7f762S7mGzMun3ViavuZ2QqJoub2Bab/IzXXWd12nS6zibbxprc39WNf6Ixp1udgvRhYFnb46XVsvHabKlmYY+h9X2VokYvORl7cDz2kpM67UYvl5nsYLVOX3VPudcdc/QyBWYPAuNfpjB6cP/UitfBwGw+/Pn7p/yymiYvE6n7XtZZF01q+rt2dfqru13UUbevuq+zTn+dXn7TxHvZyWfu7BNfMGH/dbfFOmM22Vdddceso25cTY6p5k3XZPHo3TWbnCyGQ7807WAny5qYLG5y4q2umTBZ3OnE20yYLK472dqrk8VNrrO667XEZHGdddFp/OON+fZXnTpunAejzmRxnYL0DmB5RJxMq/C8BPjJMW3WAG8GbgNeD3x+okuCpkvdg+1O2k12sFqnr06KmDpj1jkonO5CDZot1uq+R53cmGbouFMZnnc8X37oiYMu6Jo+0K7bX53toq4mi7A6/dXdLposwkpsi01OLpSIv44mJyrUMSeLK03l5hKTxSVy80yYLG46N/fDZHETx5LQvZPFTa6zEscpTe7v6sbfTZPFkxak1WU+VwA30bqT3zWZuT4irgLWZuYa4GPAdRGxCfgmraK1K9Q9cJ/OA/wSO8oSX2pv+nU29SFs8mxx0wfa3Xrg3mRcdbeLJouwEttik8mlRPx1NDlRoY45WXwQ4zYxWVanL6iXd0vk5pkwWdz0ttMPk8WT6fXJYmhunZU4TilxnNVNx5y1vkOamTcCN45ZdmXbz88C/7XZ0A7ei449ghPmH146jAn95c+cy7/fv4ONjz3J6S88ilcuX9C6q+VB+I4TjuIL92/n7oe/xbNDwxw+OMB3LjmGn3z5i57vc8dTC/nHex7lmbY/rH344ADfe9pCViw+upHXNJ7rLjuXf9/U9jpPPfjXWcfpLzyKf71/O/e0rYuXLTmGS8/99rr41/u28/UdT+8zu/fAjqd5/Jkhvv+0ha2OOjxke+mSY6qnTfzEI+a0PnJnnHDUhO1esqS592SyMTs5PG1qW/nEW8/hi5t2sHHrk5x+/FG8YpztYvmiefzrfdu45+Fdz98s4GVLjuYN373soLahOmM2rdMxJ3orrq36um/rk5w2QV9HDLbe79NfOPE2Bq3vvxyqj7/lu/ni13Zw32NPctoLj+IVp3S2Xo+cM623MugbThY3r8RkcdMH5HXMhMniunF10le3HLhPVVz9MFlcR5111uTX9DqNrYlttpPtolsmi/vySGDu4ABzGf9L5N3ktWcu5rVnNtPXJ3/25dy6cRsbHtnFisVHs/r0RfscFL7mZSdw/X98g3Wbd7J7aJi5gwOsXDafH3nZCVN+UH7RmYuhoddZx/WTrIsHdzzN7qF9v7D97NAwD+14mmPOXDxlcbIHuPkAAAi+SURBVA2PJEPHnsLQkcdz50NP7BdXv4xZ18VnLZm0zfWXnzfhezkVYzatyTFfV6Ov2QOt9XPskYONjTuZHztr/xt4aer12mTxeaccVzqESa055ZWN7XPOOflYvvi1Hfvl3betPuX5Puu0mQpNvs466rzOm+/dut9k8dd3PM2ze4c5/4zjpyw2gKPnHgZMvo2+YvmCaR+zjqbiqrNdNL3NTve2OKrOOqvTpm78Tb7fdTW5vU61Sf/sy1RZtWpVrl27tsjYM9XwSBb50Hebm+/dyjuuv2ufs8VHDA7wR5eeNWVJb3gkeePHbue2+x4lZ83miDmHsXLZfK677Nwpew9KjKnyVq9eDcCtt95aNI4SImLG/NmXqWJubladvDtTcvNkr/PDN9/PH/zLfWP/FDS/9OrTeMf5y6c0rvN+/DKGjjyeD77vndM2WTzdYzZppmyzTTI3d9GffVFZA7OC8884fspnGrvd6tMXsXLZ/P1m91afvmjKxrx14zbWbd5JDrRmfp8ZGmbd5p3cunHblL0fJcZUWcMjyTPzX8zQkcdz871bPUiQCquTd2dKbp7sdb5k8dHMHRzYZ7J47uDAlH6taHTidvvy15KzZvOO6++atsni6RyzaTNlm22KuXlyzfw1cqmHDMwKrrvsXP7o0rP4pVefxh9detaUJ4L1j+za7zLh3UPDbHhkV1+NqXLaD3J2Lv0e3nH9XbzxY7czPFL8HjaSNKnRyeIjBgcIWlcuTetkcczaZ+K2n8ZUOebmejxDqhlpumf3Ssz8lhhT5XhGXFIvG50sns5LQSeauJ2q/WaJMVWOubkez5BK06DEzG+JMVWOZ8Ql9brRyeJ3nL+c8884fsovaxyduG03XZPF0zmmyjE31+MZUmkalJj5LTGmyvGMuCR1psQ9JUqMqXLMzfVYkErTpMRNALzxwMzhQY4kdcbJYk01c3M9/tkXSeoTM/1W/P7Zl0NnbpakZpmb/bMvkjRjeEZckqTuYm6enDc1kiRJkiQVYUEqSZIkSSrCglSSJEmSVIQFqSRJkiSpCAtSSZIkSVIRxf7sS0RsBx5qqLsFwI6G+ppuvRw7GH9pxl+W8Zc1Nv4TM3NhqWD6gbn5eb0cOxh/acZflvGX1XFuLlaQNiki1vbq357r5djB+Esz/rKMv6xej7/f9fL708uxg/GXZvxlGX9ZBxO/l+xKkiRJkoqwIJUkSZIkFdEvBenVpQM4BL0cOxh/acZflvGX1evx97tefn96OXYw/tKMvyzjL6vj+PviO6SSJEmSpN7TL2dIJUmSJEk9xoJUkiRJklRETxekEXFBRGyMiE0R8e7S8XQqIh6MiHsiYl1ErC0dz2Qi4pqI2BYRX21bdmxE/EtE3F/9/4KSMU7kAPF/ICIert6DdRHxmpIxTiQilkXELRGxISLWR8QvVMu7/j2YIPaeWP8RcXhE/EdEfKWK/zeq5SdHxO3VPuivI2KwdKzjmSD+ayPi623rf2XpWCcSEQMRcVdEfKZ63BPrf6YxN08vc3NZ5uZyzM3doYnc3LMFaUQMAB8FLgRWAJdGxIqyUR2UH8jMlT3y94auBS4Ys+zdwM2ZuRy4uXrcra5l//gB/qB6D1Zm5o3THFMn9gLvyswVwMuBt1fbfC+8BweKHXpj/e8BXpWZZwIrgQsi4uXA79KK/1TgCeCygjFO5EDxA/xK2/pfVy7EWn4BuLftca+s/xnD3FzEtZibSzI3l2Nu7g6HnJt7tiAFzgE2ZeYDmTkEfAq4uHBMfS0zvwB8c8zii4FPVD9/AnjdtAbVgQPE3zMy89HM/HL185O0PvxL6IH3YILYe0K2PFU9PKz6l8CrgE9Xy7ty3cOE8feMiFgK/Ajw59XjoEfW/wxjbp5m5uayzM3lmJvLayo393JBugTY3PZ4Cz30Iaok8M8RcWdEXF46mIN0fGY+Wv38GHB8yWAO0hURcXd12VDXXVIznog4CTgLuJ0eew/GxA49sv6rS1LWAduAfwG+BuzMzL1Vk67eB42NPzNH1/9vVev/DyJiTsEQJ/Mh4FeBkerxcfTQ+p9BzM3doafywgH0RG5oZ26efubm4hrJzb1ckPaDV2bm2bQubXp7RHxf6YAORbb+hlBPzewAfwycQutSiUeBD5YNZ3IRMQ/4W+Cdmbmr/Xfd/h6ME3vPrP/MHM7MlcBSWmeBvqNwSB0ZG39EvBR4D63X8d3AscCvFQzxgCLiR4FtmXln6Vg0I5iby+uZ3DDK3FyGubmcJnNzLxekDwPL2h4vrZb1jMx8uPp/G/B/aH2Qes3WiDgBoPp/W+F4OpKZW6udwQjwZ3T5exARh9FKGn+VmX9XLe6J92C82Htt/QNk5k7gFuA8YH5EzK5+1RP7oLb4L6gu18rM3AN8nO5d/68ALoqIB2ldAvoq4A/pwfU/A5ibu0NP5IUD6bXcYG4uz9xcRGO5uZcL0juA5dWdnAaBS4A1hWOqLSKOjIijRn8Gfgj46sTP6kprgDdXP78Z+L8FY+nYaLKo/Bhd/B5U1+V/DLg3M3+/7Vdd/x4cKPZeWf8RsTAi5lc/zwVeTeu7NrcAr6+adeW6hwPG/59tB0tB6zseXbn+M/M9mbk0M0+ita//fGb+FD2y/mcYc3N36Pq8MJFeyQ1gbi7J3FxWk7k5WlcR9KZo3Yb6Q8AAcE1m/lbhkGqLiBfTmnkFmA18stvjj4jrgdXAAmAr8H7g74EbgBcBDwE/kZldeXOCA8S/mtYlKQk8CPxc23c+ukpEvBL4N+Aevn2t/ntpfd+jq9+DCWK/lB5Y/xHxnbS+mD9AayLvhsy8qvocf4rWJTV3AT9dzWh2lQni/zywEAhgHfC2thssdKWIWA38cmb+aK+s/5nG3Dy9zM1lmZvLMTd3j0PNzT1dkEqSJEmSelcvX7IrSZIkSephFqSSJEmSpCIsSCVJkiRJRViQSpIkSZKKsCCVJEmSJBVhQSpJkiRJKsKCVJIkSZJUxP8HtQiyu0Wdh9sAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 1152x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AchvsW4r-ihq",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "6b7e6c4f-723d-49a6-fc3a-f4ff1fafc2f6"
      },
      "source": [
        "# In addition, There exists autocorrelation in squared residuals, suggesting GARCH\n",
        "fig, axes = plt.subplots(1, 2, figsize=(16, 4))\n",
        "plot_acf(residuals**2, ax=axes[0])\n",
        "plot_pacf(residuals**2, ax=axes[1])\n",
        "plt.show()"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1152x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Yt76gLyx-iht",
        "colab_type": "text"
      },
      "source": [
        "#### Step Four: Forecast"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "D1e-kC7u-iht",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# The fit is on return. Errors are accumulated by cumprod\n",
        "return_predicted = arima_fitted.predict()\n",
        "price_predicted = hist_close[0]*np.cumprod(1+return_predicted/100.0)"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AxR0kJRa-ihw",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "forecasted, forecasted_std, forecasted_bounds = arima_fitted.forecast(hist_testing.shape[0])"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VsUVIFBi-ihz",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 320
        },
        "outputId": "3f0509a0-fa9d-4636-c671-1d082249981b"
      },
      "source": [
        "plt.figure(figsize=(12, 5))\n",
        "return_expected = pd.DataFrame(forecasted, index=hist_testing.index)\n",
        "return_lb = pd.DataFrame(forecasted_bounds[:, 0], index=hist_testing.index)\n",
        "return_ub = pd.DataFrame(forecasted_bounds[:, 1], index=hist_testing.index)\n",
        "plt.plot(return_expected, label='expected')\n",
        "plt.plot(hist_testing, label='actual')\n",
        "plt.fill_between(hist_testing.index, return_lb.values.reshape([-1]), return_ub.values.reshape([-1]), color='gray', alpha=0.7)\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TWgxgX0G-ih2",
        "colab_type": "text"
      },
      "source": [
        "### GARCH\n",
        "[DOC](https://arch.readthedocs.io/en/latest/)\n",
        "#### Step One: Identify Lag Orders"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d60iE2quAtwC",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 289
        },
        "outputId": "b3f884ce-537a-49b2-9beb-7d382509beb8"
      },
      "source": [
        "# !pip install arch"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Collecting arch\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/7f/5c/ef80e96f2cdc6c2d293b7e4688888a4428963c966fbb0c749c9078e68bb6/arch-4.15-cp36-cp36m-manylinux1_x86_64.whl (790kB)\n",
            "\u001b[K     |████████████████████████████████| 798kB 2.8MB/s \n",
            "\u001b[?25hCollecting property-cached>=1.6.3\n",
            "  Downloading https://files.pythonhosted.org/packages/5c/6c/94d8e520b20a2502e508e1c558f338061cf409cbee78fd6a3a5c6ae812bd/property_cached-1.6.4-py2.py3-none-any.whl\n",
            "Requirement already satisfied: cython>=0.29.14 in /usr/local/lib/python3.6/dist-packages (from arch) (0.29.20)\n",
            "Requirement already satisfied: statsmodels>=0.9 in /usr/local/lib/python3.6/dist-packages (from arch) (0.10.2)\n",
            "Requirement already satisfied: numpy>=1.14 in /usr/local/lib/python3.6/dist-packages (from arch) (1.18.5)\n",
            "Requirement already satisfied: pandas>=0.23 in /usr/local/lib/python3.6/dist-packages (from arch) (1.0.5)\n",
            "Requirement already satisfied: scipy>=1.0.1 in /usr/local/lib/python3.6/dist-packages (from arch) (1.4.1)\n",
            "Requirement already satisfied: patsy>=0.4.0 in /usr/local/lib/python3.6/dist-packages (from statsmodels>=0.9->arch) (0.5.1)\n",
            "Requirement already satisfied: pytz>=2017.2 in /usr/local/lib/python3.6/dist-packages (from pandas>=0.23->arch) (2018.9)\n",
            "Requirement already satisfied: python-dateutil>=2.6.1 in /usr/local/lib/python3.6/dist-packages (from pandas>=0.23->arch) (2.8.1)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from patsy>=0.4.0->statsmodels>=0.9->arch) (1.12.0)\n",
            "Installing collected packages: property-cached, arch\n",
            "Successfully installed arch-4.15 property-cached-1.6.4\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Cr0KRQar-ih3",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "1d63a17d-cd99-4480-ccc8-8f8f5eff5236"
      },
      "source": [
        "from arch import arch_model\n",
        "dict_aic = {}\n",
        "\n",
        "for l in range(5):\n",
        "    for p in range(1, 5):\n",
        "        for q in range(1, 5):\n",
        "            try:\n",
        "                split_date = hist_ret.index[-45]\n",
        "                model = arch_model(hist_ret, mean='ARX', lags=l, vol='Garch', p=p, o=0, q=q, dist='Normal')\n",
        "                res = model.fit(last_obs=split_date)\n",
        "                dict_aic[(l, p, q)] = res.aic\n",
        "            except:\n",
        "                pass\n",
        "\n",
        "df_aic = pd.DataFrame.from_dict(dict_aic, orient='index', columns=['aic'])\n",
        "l, p, q = df_aic[df_aic.aic == df_aic.aic.min()].index[0]\n",
        "print(f'ARIMA-GARCH order is ({l}, {p}, {q})')"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iteration:      1,   Func. Count:      6,   Neg. LLF: 7030.224152342767\n",
            "Iteration:      2,   Func. Count:     16,   Neg. LLF: 7024.528789814047\n",
            "Iteration:      3,   Func. Count:     24,   Neg. LLF: 7010.284602352095\n",
            "Iteration:      4,   Func. Count:     32,   Neg. LLF: 7004.395988477274\n",
            "Iteration:      5,   Func. Count:     39,   Neg. LLF: 6999.789356658235\n",
            "Iteration:      6,   Func. Count:     46,   Neg. LLF: 6997.441419928551\n",
            "Iteration:      7,   Func. Count:     53,   Neg. LLF: 6995.879581251908\n",
            "Iteration:      8,   Func. Count:     60,   Neg. LLF: 6994.965077274485\n",
            "Iteration:      9,   Func. Count:     66,   Neg. LLF: 6994.4796123100605\n",
            "Iteration:     10,   Func. Count:     72,   Neg. LLF: 6994.1069661181\n",
            "Iteration:     11,   Func. Count:     78,   Neg. LLF: 6994.0996327666735\n",
            "Iteration:     12,   Func. Count:     84,   Neg. LLF: 6994.099570709919\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6994.099569793737\n",
            "            Iterations: 12\n",
            "            Function evaluations: 85\n",
            "            Gradient evaluations: 12\n",
            "Iteration:      1,   Func. Count:      7,   Neg. LLF: 7028.472978832278\n",
            "Iteration:      2,   Func. Count:     20,   Neg. LLF: 7018.728699114153\n",
            "Iteration:      3,   Func. Count:     31,   Neg. LLF: 7017.965101265944\n",
            "Iteration:      4,   Func. Count:     39,   Neg. LLF: 7011.191686400371\n",
            "Iteration:      5,   Func. Count:     46,   Neg. LLF: 7007.081160316764\n",
            "Iteration:      6,   Func. Count:     54,   Neg. LLF: 7002.534949867107\n",
            "Iteration:      7,   Func. Count:     63,   Neg. LLF: 7000.825519661055\n",
            "Iteration:      8,   Func. Count:     71,   Neg. LLF: 6998.650754376121\n",
            "Iteration:      9,   Func. Count:     79,   Neg. LLF: 6995.6510477384945\n",
            "Iteration:     10,   Func. Count:     86,   Neg. LLF: 6994.140608523734\n",
            "Iteration:     11,   Func. Count:     93,   Neg. LLF: 6994.102858029197\n",
            "Iteration:     12,   Func. Count:    100,   Neg. LLF: 6994.099581272058\n",
            "Iteration:     13,   Func. Count:    107,   Neg. LLF: 6994.09957108977\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6994.099569801524\n",
            "            Iterations: 13\n",
            "            Function evaluations: 108\n",
            "            Gradient evaluations: 13\n",
            "Iteration:      1,   Func. Count:      8,   Neg. LLF: 7035.163723783372\n",
            "Iteration:      2,   Func. Count:     22,   Neg. LLF: 7027.325797355\n",
            "Iteration:      3,   Func. Count:     35,   Neg. LLF: 7027.311702975774\n",
            "Iteration:      4,   Func. Count:     44,   Neg. LLF: 7020.270953351868\n",
            "Iteration:      5,   Func. Count:     53,   Neg. LLF: 7013.172638059708\n",
            "Iteration:      6,   Func. Count:     62,   Neg. LLF: 7008.627903250872\n",
            "Iteration:      7,   Func. Count:     72,   Neg. LLF: 7007.530465664683\n",
            "Iteration:      8,   Func. Count:     80,   Neg. LLF: 6995.042704916223\n",
            "Iteration:      9,   Func. Count:     89,   Neg. LLF: 6994.543626583247\n",
            "Iteration:     10,   Func. Count:     98,   Neg. LLF: 6994.1938199721\n",
            "Iteration:     11,   Func. Count:    106,   Neg. LLF: 6994.103878678574\n",
            "Iteration:     12,   Func. Count:    114,   Neg. LLF: 6994.100388588333\n",
            "Iteration:     13,   Func. Count:    122,   Neg. LLF: 6994.099697482954\n",
            "Iteration:     14,   Func. Count:    130,   Neg. LLF: 6994.099570808873\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6994.099569781504\n",
            "            Iterations: 14\n",
            "            Function evaluations: 131\n",
            "            Gradient evaluations: 14\n",
            "Iteration:      1,   Func. Count:      9,   Neg. LLF: 7051.484221070977\n",
            "Iteration:      2,   Func. Count:     23,   Neg. LLF: 7046.8895087584515\n",
            "Iteration:      3,   Func. Count:     33,   Neg. LLF: 7037.707224460621\n",
            "Iteration:      4,   Func. Count:     43,   Neg. LLF: 7034.813175687646\n",
            "Iteration:      5,   Func. Count:     54,   Neg. LLF: 7033.201747066029\n",
            "Iteration:      6,   Func. Count:     64,   Neg. LLF: 7010.392150729051\n",
            "Iteration:      7,   Func. Count:     74,   Neg. LLF: 7005.275202571335\n",
            "Iteration:      8,   Func. Count:     86,   Neg. LLF: 7005.1755894829\n",
            "Iteration:      9,   Func. Count:     96,   Neg. LLF: 7002.691206156576\n",
            "Iteration:     10,   Func. Count:    105,   Neg. LLF: 6994.342158532694\n",
            "Iteration:     11,   Func. Count:    115,   Neg. LLF: 6994.161154357976\n",
            "Iteration:     12,   Func. Count:    124,   Neg. LLF: 6994.105149898323\n",
            "Iteration:     13,   Func. Count:    133,   Neg. LLF: 6994.099842293655\n",
            "Iteration:     14,   Func. Count:    142,   Neg. LLF: 6994.0995756719285\n",
            "Iteration:     15,   Func. Count:    151,   Neg. LLF: 6994.099571319004\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6994.099569818311\n",
            "            Iterations: 15\n",
            "            Function evaluations: 152\n",
            "            Gradient evaluations: 15\n",
            "Iteration:      1,   Func. Count:      7,   Neg. LLF: 7009.9998122171\n",
            "Iteration:      2,   Func. Count:     20,   Neg. LLF: 6998.235331791097\n",
            "Iteration:      3,   Func. Count:     31,   Neg. LLF: 6996.570818957945\n",
            "Iteration:      4,   Func. Count:     39,   Neg. LLF: 6992.519019905625\n",
            "Iteration:      5,   Func. Count:     48,   Neg. LLF: 6991.6221269012585\n",
            "Iteration:      6,   Func. Count:     56,   Neg. LLF: 6990.308326615184\n",
            "Iteration:      7,   Func. Count:     64,   Neg. LLF: 6989.597140502956\n",
            "Iteration:      8,   Func. Count:     72,   Neg. LLF: 6989.210225976816\n",
            "Iteration:      9,   Func. Count:     80,   Neg. LLF: 6988.642657472305\n",
            "Iteration:     10,   Func. Count:     88,   Neg. LLF: 6988.595259301679\n",
            "Iteration:     11,   Func. Count:     95,   Neg. LLF: 6988.562636052056\n",
            "Iteration:     12,   Func. Count:    102,   Neg. LLF: 6988.562154696661\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6988.562153794233\n",
            "            Iterations: 12\n",
            "            Function evaluations: 103\n",
            "            Gradient evaluations: 12\n",
            "Iteration:      1,   Func. Count:      8,   Neg. LLF: 6997.2117621360685\n",
            "Iteration:      2,   Func. Count:     22,   Neg. LLF: 6988.7383731625705\n",
            "Iteration:      3,   Func. Count:     35,   Neg. LLF: 6988.703150393654\n",
            "Iteration:      4,   Func. Count:     46,   Neg. LLF: 6988.452262625733\n",
            "Iteration:      5,   Func. Count:     56,   Neg. LLF: 6988.269093776369\n",
            "Iteration:      6,   Func. Count:     65,   Neg. LLF: 6987.677170371192\n",
            "Iteration:      7,   Func. Count:     74,   Neg. LLF: 6987.636504017606\n",
            "Iteration:      8,   Func. Count:     84,   Neg. LLF: 6987.585911684404\n",
            "Iteration:      9,   Func. Count:     92,   Neg. LLF: 6987.56477004843\n",
            "Iteration:     10,   Func. Count:    100,   Neg. LLF: 6987.554234027405\n",
            "Iteration:     11,   Func. Count:    108,   Neg. LLF: 6987.552897328387\n",
            "Iteration:     12,   Func. Count:    116,   Neg. LLF: 6987.552850727576\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6987.552849940373\n",
            "            Iterations: 12\n",
            "            Function evaluations: 117\n",
            "            Gradient evaluations: 12\n",
            "Iteration:      1,   Func. Count:      9,   Neg. LLF: 7001.6412927743995\n",
            "Iteration:      2,   Func. Count:     22,   Neg. LLF: 6997.812179855611\n",
            "Iteration:      3,   Func. Count:     33,   Neg. LLF: 6997.426607509056\n",
            "Iteration:      4,   Func. Count:     44,   Neg. LLF: 6991.862059345052\n",
            "Iteration:      5,   Func. Count:     55,   Neg. LLF: 6991.677025343002\n",
            "Iteration:      6,   Func. Count:     65,   Neg. LLF: 6991.442512527119\n",
            "Iteration:      7,   Func. Count:     75,   Neg. LLF: 6990.579529267405\n",
            "Iteration:      8,   Func. Count:     85,   Neg. LLF: 6989.9807425407325\n",
            "Iteration:      9,   Func. Count:     95,   Neg. LLF: 6989.606017508138\n",
            "Iteration:     10,   Func. Count:    105,   Neg. LLF: 6988.473054104817\n",
            "Iteration:     11,   Func. Count:    115,   Neg. LLF: 6988.292757468966\n",
            "Iteration:     12,   Func. Count:    125,   Neg. LLF: 6987.9880082488635\n",
            "Iteration:     13,   Func. Count:    134,   Neg. LLF: 6987.58616902714\n",
            "Iteration:     14,   Func. Count:    144,   Neg. LLF: 6987.560328249401\n",
            "Iteration:     15,   Func. Count:    153,   Neg. LLF: 6987.556615812802\n",
            "Iteration:     16,   Func. Count:    162,   Neg. LLF: 6987.55295018627\n",
            "Iteration:     17,   Func. Count:    171,   Neg. LLF: 6987.552853230111\n",
            "Iteration:     18,   Func. Count:    180,   Neg. LLF: 6987.552850056254\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6987.5528499519205\n",
            "            Iterations: 18\n",
            "            Function evaluations: 180\n",
            "            Gradient evaluations: 18\n",
            "Iteration:      1,   Func. Count:     10,   Neg. LLF: 7011.714429660553\n",
            "Iteration:      2,   Func. Count:     24,   Neg. LLF: 7006.589961254755\n",
            "Iteration:      3,   Func. Count:     36,   Neg. LLF: 7005.807310025979\n",
            "Iteration:      4,   Func. Count:     47,   Neg. LLF: 7001.277559196602\n",
            "Iteration:      5,   Func. Count:     59,   Neg. LLF: 7000.428780126329\n",
            "Iteration:      6,   Func. Count:     71,   Neg. LLF: 7000.175363675116\n",
            "Iteration:      7,   Func. Count:     82,   Neg. LLF: 6996.269685377037\n",
            "Iteration:      8,   Func. Count:     93,   Neg. LLF: 6994.183023444264\n",
            "Iteration:      9,   Func. Count:    104,   Neg. LLF: 6992.581971320902\n",
            "Iteration:     10,   Func. Count:    115,   Neg. LLF: 6989.835931047655\n",
            "Iteration:     11,   Func. Count:    126,   Neg. LLF: 6989.007837703777\n",
            "Iteration:     12,   Func. Count:    137,   Neg. LLF: 6988.5142167699205\n",
            "Iteration:     13,   Func. Count:    148,   Neg. LLF: 6988.156274035819\n",
            "Iteration:     14,   Func. Count:    158,   Neg. LLF: 6987.660259493722\n",
            "Iteration:     15,   Func. Count:    168,   Neg. LLF: 6987.569337501821\n",
            "Iteration:     16,   Func. Count:    178,   Neg. LLF: 6987.556287934012\n",
            "Iteration:     17,   Func. Count:    188,   Neg. LLF: 6987.552961254207\n",
            "Iteration:     18,   Func. Count:    198,   Neg. LLF: 6987.552850785432\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6987.552849949123\n",
            "            Iterations: 18\n",
            "            Function evaluations: 199\n",
            "            Gradient evaluations: 18\n",
            "Iteration:      1,   Func. Count:      8,   Neg. LLF: 7009.038980526184\n",
            "Iteration:      2,   Func. Count:     22,   Neg. LLF: 6999.293201194214\n",
            "Iteration:      3,   Func. Count:     34,   Neg. LLF: 6997.791672309357\n",
            "Iteration:      4,   Func. Count:     45,   Neg. LLF: 6997.685282620003\n",
            "Iteration:      5,   Func. Count:     55,   Neg. LLF: 6997.215325134669\n",
            "Iteration:      6,   Func. Count:     64,   Neg. LLF: 6996.057495397079\n",
            "Iteration:      7,   Func. Count:     73,   Neg. LLF: 6991.688428557296\n",
            "Iteration:      8,   Func. Count:     82,   Neg. LLF: 6990.880638806139\n",
            "Iteration:      9,   Func. Count:     91,   Neg. LLF: 6990.612022737912\n",
            "Iteration:     10,   Func. Count:     99,   Neg. LLF: 6989.131000950497\n",
            "Iteration:     11,   Func. Count:    107,   Neg. LLF: 6988.723749555864\n",
            "Iteration:     12,   Func. Count:    115,   Neg. LLF: 6988.566686354481\n",
            "Iteration:     13,   Func. Count:    123,   Neg. LLF: 6988.562330174251\n",
            "Iteration:     14,   Func. Count:    131,   Neg. LLF: 6988.562167139009\n",
            "Iteration:     15,   Func. Count:    139,   Neg. LLF: 6988.562154140302\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6988.562154139038\n",
            "            Iterations: 15\n",
            "            Function evaluations: 139\n",
            "            Gradient evaluations: 15\n",
            "Iteration:      1,   Func. Count:      9,   Neg. LLF: 7004.116182678201\n",
            "Iteration:      2,   Func. Count:     24,   Neg. LLF: 6997.108931572454\n",
            "Iteration:      3,   Func. Count:     38,   Neg. LLF: 6997.077426010184\n",
            "Iteration:      4,   Func. Count:     49,   Neg. LLF: 6996.165361747238\n",
            "Iteration:      5,   Func. Count:     60,   Neg. LLF: 6991.971126233462\n",
            "Iteration:      6,   Func. Count:     71,   Neg. LLF: 6991.324816115488\n",
            "Iteration:      7,   Func. Count:     81,   Neg. LLF: 6989.253545673543\n",
            "Iteration:      8,   Func. Count:     91,   Neg. LLF: 6988.142239604507\n",
            "Iteration:      9,   Func. Count:    101,   Neg. LLF: 6987.6294938361425\n",
            "Iteration:     10,   Func. Count:    111,   Neg. LLF: 6987.282732450187\n",
            "Iteration:     11,   Func. Count:    121,   Neg. LLF: 6987.186128346279\n",
            "Iteration:     12,   Func. Count:    131,   Neg. LLF: 6987.155154686466\n",
            "Iteration:     13,   Func. Count:    141,   Neg. LLF: 6987.126248442268\n",
            "Iteration:     14,   Func. Count:    150,   Neg. LLF: 6987.119706308322\n",
            "Iteration:     15,   Func. Count:    159,   Neg. LLF: 6987.117234108899\n",
            "Iteration:     16,   Func. Count:    168,   Neg. LLF: 6987.117083231284\n",
            "Iteration:     17,   Func. Count:    177,   Neg. LLF: 6987.117078395557\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6987.117078396339\n",
            "            Iterations: 17\n",
            "            Function evaluations: 177\n",
            "            Gradient evaluations: 17\n",
            "Iteration:      1,   Func. Count:     10,   Neg. LLF: 7008.3107216277895\n",
            "Iteration:      2,   Func. Count:     24,   Neg. LLF: 7003.3482841509995\n",
            "Iteration:      3,   Func. Count:     36,   Neg. LLF: 6998.396487588159\n",
            "Iteration:      4,   Func. Count:     48,   Neg. LLF: 6993.79225798315\n",
            "Iteration:      5,   Func. Count:     60,   Neg. LLF: 6991.853849739908\n",
            "Iteration:      6,   Func. Count:     72,   Neg. LLF: 6990.112456922295\n",
            "Iteration:      7,   Func. Count:     84,   Neg. LLF: 6989.766531175724\n",
            "Iteration:      8,   Func. Count:     95,   Neg. LLF: 6989.277768247539\n",
            "Iteration:      9,   Func. Count:    106,   Neg. LLF: 6988.662398949196\n",
            "Iteration:     10,   Func. Count:    117,   Neg. LLF: 6988.360797991136\n",
            "Iteration:     11,   Func. Count:    128,   Neg. LLF: 6987.959201731934\n",
            "Iteration:     12,   Func. Count:    139,   Neg. LLF: 6987.651590251611\n",
            "Iteration:     13,   Func. Count:    150,   Neg. LLF: 6987.412119929425\n",
            "Iteration:     14,   Func. Count:    161,   Neg. LLF: 6987.3016570553345\n",
            "Iteration:     15,   Func. Count:    172,   Neg. LLF: 6987.244491063251\n",
            "Iteration:     16,   Func. Count:    183,   Neg. LLF: 6987.179641558356\n",
            "Iteration:     17,   Func. Count:    193,   Neg. LLF: 6987.130739983184\n",
            "Iteration:     18,   Func. Count:    204,   Neg. LLF: 6987.123002756697\n",
            "Iteration:     19,   Func. Count:    214,   Neg. LLF: 6987.118311609476\n",
            "Iteration:     20,   Func. Count:    224,   Neg. LLF: 6987.1171970078485\n",
            "Iteration:     21,   Func. Count:    234,   Neg. LLF: 6987.117078963998\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6987.117078206969\n",
            "            Iterations: 21\n",
            "            Function evaluations: 235\n",
            "            Gradient evaluations: 21\n",
            "Iteration:      1,   Func. Count:     11,   Neg. LLF: 7017.516466091842\n",
            "Iteration:      2,   Func. Count:     26,   Neg. LLF: 7012.658379680461\n",
            "Iteration:      3,   Func. Count:     39,   Neg. LLF: 7010.825796066133\n",
            "Iteration:      4,   Func. Count:     51,   Neg. LLF: 6997.6547619203375\n",
            "Iteration:      5,   Func. Count:     64,   Neg. LLF: 6993.197277750482\n",
            "Iteration:      6,   Func. Count:     77,   Neg. LLF: 6992.896193285986\n",
            "Iteration:      7,   Func. Count:     89,   Neg. LLF: 6990.932450025697\n",
            "Iteration:      8,   Func. Count:    101,   Neg. LLF: 6989.2307285059505\n",
            "Iteration:      9,   Func. Count:    114,   Neg. LLF: 6989.16993972017\n",
            "Iteration:     10,   Func. Count:    126,   Neg. LLF: 6988.516702511285\n",
            "Iteration:     11,   Func. Count:    138,   Neg. LLF: 6987.721181629472\n",
            "Iteration:     12,   Func. Count:    150,   Neg. LLF: 6987.420991538005\n",
            "Iteration:     13,   Func. Count:    162,   Neg. LLF: 6987.313778203348\n",
            "Iteration:     14,   Func. Count:    174,   Neg. LLF: 6987.152742549493\n",
            "Iteration:     15,   Func. Count:    185,   Neg. LLF: 6987.131198940962\n",
            "Iteration:     16,   Func. Count:    197,   Neg. LLF: 6987.115190449817\n",
            "Iteration:     17,   Func. Count:    209,   Neg. LLF: 6987.111182657474\n",
            "Iteration:     18,   Func. Count:    220,   Neg. LLF: 6987.111035048779\n",
            "Iteration:     19,   Func. Count:    231,   Neg. LLF: 6987.111027299069\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6987.111027300025\n",
            "            Iterations: 19\n",
            "            Function evaluations: 231\n",
            "            Gradient evaluations: 19\n",
            "Iteration:      1,   Func. Count:      9,   Neg. LLF: 7013.255836696233\n",
            "Iteration:      2,   Func. Count:     24,   Neg. LLF: 7004.393506182361\n",
            "Iteration:      3,   Func. Count:     37,   Neg. LLF: 7003.411213039376\n",
            "Iteration:      4,   Func. Count:     48,   Neg. LLF: 6999.2983166769445\n",
            "Iteration:      5,   Func. Count:     59,   Neg. LLF: 6998.9285404265775\n",
            "Iteration:      6,   Func. Count:     69,   Neg. LLF: 6997.362041475091\n",
            "Iteration:      7,   Func. Count:     79,   Neg. LLF: 6992.801759571332\n",
            "Iteration:      8,   Func. Count:     89,   Neg. LLF: 6992.0300429807085\n",
            "Iteration:      9,   Func. Count:     98,   Neg. LLF: 6990.771801595523\n",
            "Iteration:     10,   Func. Count:    107,   Neg. LLF: 6989.544671341166\n",
            "Iteration:     11,   Func. Count:    118,   Neg. LLF: 6989.421037761499\n",
            "Iteration:     12,   Func. Count:    128,   Neg. LLF: 6988.774732765397\n",
            "Iteration:     13,   Func. Count:    137,   Neg. LLF: 6988.633493378575\n",
            "Iteration:     14,   Func. Count:    146,   Neg. LLF: 6988.60675278106\n",
            "Iteration:     15,   Func. Count:    155,   Neg. LLF: 6988.587492808923\n",
            "Iteration:     16,   Func. Count:    164,   Neg. LLF: 6988.562647739094\n",
            "Iteration:     17,   Func. Count:    173,   Neg. LLF: 6988.562177473611\n",
            "Iteration:     18,   Func. Count:    182,   Neg. LLF: 6988.56215413003\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6988.562154130616\n",
            "            Iterations: 18\n",
            "            Function evaluations: 182\n",
            "            Gradient evaluations: 18\n",
            "Iteration:      1,   Func. Count:     10,   Neg. LLF: 7010.721819785312\n",
            "Iteration:      2,   Func. Count:     26,   Neg. LLF: 7004.301946949849\n",
            "Iteration:      3,   Func. Count:     41,   Neg. LLF: 7004.292239498934\n",
            "Iteration:      4,   Func. Count:     53,   Neg. LLF: 6996.485714189598\n",
            "Iteration:      5,   Func. Count:     65,   Neg. LLF: 6995.6603641969905\n",
            "Iteration:      6,   Func. Count:     77,   Neg. LLF: 6992.028179800348\n",
            "Iteration:      7,   Func. Count:     88,   Neg. LLF: 6990.179585587764\n",
            "Iteration:      8,   Func. Count:     99,   Neg. LLF: 6988.4855187785415\n",
            "Iteration:      9,   Func. Count:    110,   Neg. LLF: 6988.179680258836\n",
            "Iteration:     10,   Func. Count:    121,   Neg. LLF: 6987.516994601029\n",
            "Iteration:     11,   Func. Count:    132,   Neg. LLF: 6987.273932559097\n",
            "Iteration:     12,   Func. Count:    143,   Neg. LLF: 6987.231496878327\n",
            "Iteration:     13,   Func. Count:    155,   Neg. LLF: 6987.229035888675\n",
            "Iteration:     14,   Func. Count:    166,   Neg. LLF: 6987.145377662668\n",
            "Iteration:     15,   Func. Count:    176,   Neg. LLF: 6987.129841139771\n",
            "Iteration:     16,   Func. Count:    186,   Neg. LLF: 6987.117322318387\n",
            "Iteration:     17,   Func. Count:    196,   Neg. LLF: 6987.116479455841\n",
            "Iteration:     18,   Func. Count:    206,   Neg. LLF: 6987.116133555661\n",
            "Iteration:     19,   Func. Count:    216,   Neg. LLF: 6987.116131746565\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6987.11613174725\n",
            "            Iterations: 19\n",
            "            Function evaluations: 216\n",
            "            Gradient evaluations: 19\n",
            "Iteration:      1,   Func. Count:     11,   Neg. LLF: 7016.153110537136\n",
            "Iteration:      2,   Func. Count:     27,   Neg. LLF: 7010.740311808464\n",
            "Iteration:      3,   Func. Count:     40,   Neg. LLF: 7002.494223624238\n",
            "Iteration:      4,   Func. Count:     52,   Neg. LLF: 6990.413964137195\n",
            "Iteration:      5,   Func. Count:     65,   Neg. LLF: 6988.794578957387\n",
            "Iteration:      6,   Func. Count:     78,   Neg. LLF: 6988.699640360226\n",
            "Iteration:      7,   Func. Count:     91,   Neg. LLF: 6988.581157017823\n",
            "Iteration:      8,   Func. Count:    103,   Neg. LLF: 6988.0352754934665\n",
            "Iteration:      9,   Func. Count:    116,   Neg. LLF: 6987.876677301429\n",
            "Iteration:     10,   Func. Count:    129,   Neg. LLF: 6987.867178531982\n",
            "Iteration:     11,   Func. Count:    142,   Neg. LLF: 6987.816005897349\n",
            "Iteration:     12,   Func. Count:    153,   Neg. LLF: 6987.311519025367\n",
            "Iteration:     13,   Func. Count:    164,   Neg. LLF: 6986.982724035775\n",
            "Iteration:     14,   Func. Count:    176,   Neg. LLF: 6986.9031922429\n",
            "Iteration:     15,   Func. Count:    187,   Neg. LLF: 6986.844094077478\n",
            "Iteration:     16,   Func. Count:    198,   Neg. LLF: 6986.842195045316\n",
            "Iteration:     17,   Func. Count:    209,   Neg. LLF: 6986.841810921921\n",
            "Iteration:     18,   Func. Count:    220,   Neg. LLF: 6986.841776211049\n",
            "Iteration:     19,   Func. Count:    231,   Neg. LLF: 6986.841775022324\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6986.841775021984\n",
            "            Iterations: 19\n",
            "            Function evaluations: 231\n",
            "            Gradient evaluations: 19\n",
            "Iteration:      1,   Func. Count:     12,   Neg. LLF: 7023.602633095564\n",
            "Iteration:      2,   Func. Count:     29,   Neg. LLF: 7018.562900708062\n",
            "Iteration:      3,   Func. Count:     42,   Neg. LLF: 7006.567240623865\n",
            "Iteration:      4,   Func. Count:     55,   Neg. LLF: 6999.17530869391\n",
            "Iteration:      5,   Func. Count:     69,   Neg. LLF: 6994.1062295662905\n",
            "Iteration:      6,   Func. Count:     83,   Neg. LLF: 6992.277803289169\n",
            "Iteration:      7,   Func. Count:     97,   Neg. LLF: 6991.397000312757\n",
            "Iteration:      8,   Func. Count:    111,   Neg. LLF: 6990.59504967061\n",
            "Iteration:      9,   Func. Count:    125,   Neg. LLF: 6990.365299973804\n",
            "Iteration:     10,   Func. Count:    138,   Neg. LLF: 6988.401339955262\n",
            "Iteration:     11,   Func. Count:    151,   Neg. LLF: 6987.326857573265\n",
            "Iteration:     12,   Func. Count:    164,   Neg. LLF: 6986.70372211175\n",
            "Iteration:     13,   Func. Count:    177,   Neg. LLF: 6986.610397364426\n",
            "Iteration:     14,   Func. Count:    190,   Neg. LLF: 6986.578348678404\n",
            "Iteration:     15,   Func. Count:    203,   Neg. LLF: 6986.574008959471\n",
            "Iteration:     16,   Func. Count:    216,   Neg. LLF: 6986.568295262025\n",
            "Iteration:     17,   Func. Count:    229,   Neg. LLF: 6986.567520335903\n",
            "Iteration:     18,   Func. Count:    241,   Neg. LLF: 6986.5660862611185\n",
            "Iteration:     19,   Func. Count:    253,   Neg. LLF: 6986.562657491343\n",
            "Iteration:     20,   Func. Count:    265,   Neg. LLF: 6986.534392440646\n",
            "Iteration:     21,   Func. Count:    277,   Neg. LLF: 6986.5224040245785\n",
            "Iteration:     22,   Func. Count:    289,   Neg. LLF: 6986.513851897269\n",
            "Iteration:     23,   Func. Count:    301,   Neg. LLF: 6986.5091791983305\n",
            "Iteration:     24,   Func. Count:    313,   Neg. LLF: 6986.508686182924\n",
            "Iteration:     25,   Func. Count:    325,   Neg. LLF: 6986.50860764639\n",
            "Iteration:     26,   Func. Count:    337,   Neg. LLF: 6986.508600160562\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6986.508600160668\n",
            "            Iterations: 26\n",
            "            Function evaluations: 337\n",
            "            Gradient evaluations: 26\n",
            "Iteration:      1,   Func. Count:      7,   Neg. LLF: 7024.047550631529\n",
            "Iteration:      2,   Func. Count:     18,   Neg. LLF: 7016.766921745078\n",
            "Iteration:      3,   Func. Count:     29,   Neg. LLF: 7015.390415574579\n",
            "Iteration:      4,   Func. Count:     38,   Neg. LLF: 7003.041996919913\n",
            "Iteration:      5,   Func. Count:     47,   Neg. LLF: 6992.353170809966\n",
            "Iteration:      6,   Func. Count:     56,   Neg. LLF: 6991.1696521945\n",
            "Iteration:      7,   Func. Count:     64,   Neg. LLF: 6986.8581795012415\n",
            "Iteration:      8,   Func. Count:     72,   Neg. LLF: 6984.196488839714\n",
            "Iteration:      9,   Func. Count:     80,   Neg. LLF: 6982.576251200091\n",
            "Iteration:     10,   Func. Count:     89,   Neg. LLF: 6982.4047409707655\n",
            "Iteration:     11,   Func. Count:     96,   Neg. LLF: 6981.990005889818\n",
            "Iteration:     12,   Func. Count:    103,   Neg. LLF: 6981.763004058818\n",
            "Iteration:     13,   Func. Count:    110,   Neg. LLF: 6981.748004245215\n",
            "Iteration:     14,   Func. Count:    117,   Neg. LLF: 6981.745242395265\n",
            "Iteration:     15,   Func. Count:    124,   Neg. LLF: 6981.745223016924\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6981.74522301627\n",
            "            Iterations: 15\n",
            "            Function evaluations: 124\n",
            "            Gradient evaluations: 15\n",
            "Iteration:      1,   Func. Count:      8,   Neg. LLF: 7025.016305181214\n",
            "Iteration:      2,   Func. Count:     22,   Neg. LLF: 7008.500430634019\n",
            "Iteration:      3,   Func. Count:     34,   Neg. LLF: 7006.432594341543\n",
            "Iteration:      4,   Func. Count:     43,   Neg. LLF: 6999.645919608038\n",
            "Iteration:      5,   Func. Count:     52,   Neg. LLF: 6996.051121544726\n",
            "Iteration:      6,   Func. Count:     61,   Neg. LLF: 6992.768963427279\n",
            "Iteration:      7,   Func. Count:     69,   Neg. LLF: 6989.7327978648855\n",
            "Iteration:      8,   Func. Count:     79,   Neg. LLF: 6989.026025706487\n",
            "Iteration:      9,   Func. Count:     88,   Neg. LLF: 6984.164215404569\n",
            "Iteration:     10,   Func. Count:     98,   Neg. LLF: 6983.880729876746\n",
            "Iteration:     11,   Func. Count:    106,   Neg. LLF: 6983.30361212362\n",
            "Iteration:     12,   Func. Count:    114,   Neg. LLF: 6981.847070577254\n",
            "Iteration:     13,   Func. Count:    122,   Neg. LLF: 6981.7687175562305\n",
            "Iteration:     14,   Func. Count:    130,   Neg. LLF: 6981.746730361801\n",
            "Iteration:     15,   Func. Count:    138,   Neg. LLF: 6981.745234547043\n",
            "Iteration:     16,   Func. Count:    146,   Neg. LLF: 6981.745223620393\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6981.7452232517535\n",
            "            Iterations: 16\n",
            "            Function evaluations: 146\n",
            "            Gradient evaluations: 16\n",
            "Iteration:      1,   Func. Count:      9,   Neg. LLF: 7031.758198724158\n",
            "Iteration:      2,   Func. Count:     24,   Neg. LLF: 7017.123026524065\n",
            "Iteration:      3,   Func. Count:     37,   Neg. LLF: 7016.307408029164\n",
            "Iteration:      4,   Func. Count:     49,   Neg. LLF: 7016.140033185915\n",
            "Iteration:      5,   Func. Count:     59,   Neg. LLF: 7008.825203897986\n",
            "Iteration:      6,   Func. Count:     69,   Neg. LLF: 7001.287117052807\n",
            "Iteration:      7,   Func. Count:     79,   Neg. LLF: 6997.491109385659\n",
            "Iteration:      8,   Func. Count:     89,   Neg. LLF: 6994.811045569875\n",
            "Iteration:      9,   Func. Count:     99,   Neg. LLF: 6991.709953878666\n",
            "Iteration:     10,   Func. Count:    108,   Neg. LLF: 6981.8938969742085\n",
            "Iteration:     11,   Func. Count:    118,   Neg. LLF: 6981.791088024847\n",
            "Iteration:     12,   Func. Count:    128,   Neg. LLF: 6981.747773509057\n",
            "Iteration:     13,   Func. Count:    137,   Neg. LLF: 6981.746723250219\n",
            "Iteration:     14,   Func. Count:    146,   Neg. LLF: 6981.745398485546\n",
            "Iteration:     15,   Func. Count:    155,   Neg. LLF: 6981.74525330652\n",
            "Iteration:     16,   Func. Count:    164,   Neg. LLF: 6981.745223570253\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6981.7452230341405\n",
            "            Iterations: 16\n",
            "            Function evaluations: 164\n",
            "            Gradient evaluations: 16\n",
            "Iteration:      1,   Func. Count:     10,   Neg. LLF: 7047.601003415424\n",
            "Iteration:      2,   Func. Count:     26,   Neg. LLF: 7034.7106402820755\n",
            "Iteration:      3,   Func. Count:     40,   Neg. LLF: 7033.557191901488\n",
            "Iteration:      4,   Func. Count:     51,   Neg. LLF: 7024.353249849861\n",
            "Iteration:      5,   Func. Count:     63,   Neg. LLF: 7021.740709427727\n",
            "Iteration:      6,   Func. Count:     75,   Neg. LLF: 7021.14526706306\n",
            "Iteration:      7,   Func. Count:     85,   Neg. LLF: 6988.760959594803\n",
            "Iteration:      8,   Func. Count:     97,   Neg. LLF: 6987.248668248515\n",
            "Iteration:      9,   Func. Count:    109,   Neg. LLF: 6984.349549881072\n",
            "Iteration:     10,   Func. Count:    119,   Neg. LLF: 6982.1305521042505\n",
            "Iteration:     11,   Func. Count:    129,   Neg. LLF: 6981.7798981401875\n",
            "Iteration:     12,   Func. Count:    139,   Neg. LLF: 6981.745746997707\n",
            "Iteration:     13,   Func. Count:    149,   Neg. LLF: 6981.745228185873\n",
            "Iteration:     14,   Func. Count:    159,   Neg. LLF: 6981.745223697565\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6981.745222970434\n",
            "            Iterations: 14\n",
            "            Function evaluations: 159\n",
            "            Gradient evaluations: 14\n",
            "Iteration:      1,   Func. Count:      8,   Neg. LLF: 7006.97317389151\n",
            "Iteration:      2,   Func. Count:     22,   Neg. LLF: 6987.897777839594\n",
            "Iteration:      3,   Func. Count:     34,   Neg. LLF: 6984.530524480252\n",
            "Iteration:      4,   Func. Count:     46,   Neg. LLF: 6984.198373503954\n",
            "Iteration:      5,   Func. Count:     55,   Neg. LLF: 6980.03875522877\n",
            "Iteration:      6,   Func. Count:     64,   Neg. LLF: 6978.763051103988\n",
            "Iteration:      7,   Func. Count:     73,   Neg. LLF: 6977.349337693965\n",
            "Iteration:      8,   Func. Count:     82,   Neg. LLF: 6977.005719018907\n",
            "Iteration:      9,   Func. Count:     92,   Neg. LLF: 6976.660714616968\n",
            "Iteration:     10,   Func. Count:    101,   Neg. LLF: 6976.480557616695\n",
            "Iteration:     11,   Func. Count:    110,   Neg. LLF: 6975.950146789304\n",
            "Iteration:     12,   Func. Count:    119,   Neg. LLF: 6975.940336691519\n",
            "Iteration:     13,   Func. Count:    128,   Neg. LLF: 6975.927939944284\n",
            "Iteration:     14,   Func. Count:    136,   Neg. LLF: 6975.927787806544\n",
            "Iteration:     15,   Func. Count:    144,   Neg. LLF: 6975.927785290076\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6975.9277852902715\n",
            "            Iterations: 15\n",
            "            Function evaluations: 144\n",
            "            Gradient evaluations: 15\n",
            "Iteration:      1,   Func. Count:      9,   Neg. LLF: 6993.036980682582\n",
            "Iteration:      2,   Func. Count:     24,   Neg. LLF: 6977.158114879225\n",
            "Iteration:      3,   Func. Count:     37,   Neg. LLF: 6976.306712486569\n",
            "Iteration:      4,   Func. Count:     49,   Neg. LLF: 6975.890835551691\n",
            "Iteration:      5,   Func. Count:     60,   Neg. LLF: 6975.711290884898\n",
            "Iteration:      6,   Func. Count:     72,   Neg. LLF: 6975.689018522677\n",
            "Iteration:      7,   Func. Count:     82,   Neg. LLF: 6974.99884108615\n",
            "Iteration:      8,   Func. Count:     92,   Neg. LLF: 6974.93456632293\n",
            "Iteration:      9,   Func. Count:    102,   Neg. LLF: 6974.885530234062\n",
            "Iteration:     10,   Func. Count:    112,   Neg. LLF: 6974.839435064846\n",
            "Iteration:     11,   Func. Count:    122,   Neg. LLF: 6974.80653333306\n",
            "Iteration:     12,   Func. Count:    131,   Neg. LLF: 6974.806221108108\n",
            "Iteration:     13,   Func. Count:    140,   Neg. LLF: 6974.806177879662\n",
            "Iteration:     14,   Func. Count:    149,   Neg. LLF: 6974.806176776496\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6974.806176777039\n",
            "            Iterations: 14\n",
            "            Function evaluations: 149\n",
            "            Gradient evaluations: 14\n",
            "Iteration:      1,   Func. Count:     10,   Neg. LLF: 6996.785306518666\n",
            "Iteration:      2,   Func. Count:     25,   Neg. LLF: 6982.9556774534285\n",
            "Iteration:      3,   Func. Count:     39,   Neg. LLF: 6981.904853600747\n",
            "Iteration:      4,   Func. Count:     52,   Neg. LLF: 6981.127473065724\n",
            "Iteration:      5,   Func. Count:     64,   Neg. LLF: 6978.509296201397\n",
            "Iteration:      6,   Func. Count:     76,   Neg. LLF: 6978.402622848348\n",
            "Iteration:      7,   Func. Count:     87,   Neg. LLF: 6977.77690856897\n",
            "Iteration:      8,   Func. Count:     98,   Neg. LLF: 6977.178997706804\n",
            "Iteration:      9,   Func. Count:    109,   Neg. LLF: 6976.401874781883\n",
            "Iteration:     10,   Func. Count:    120,   Neg. LLF: 6976.028640154454\n",
            "Iteration:     11,   Func. Count:    131,   Neg. LLF: 6975.512521788962\n",
            "Iteration:     12,   Func. Count:    142,   Neg. LLF: 6975.176757465751\n",
            "Iteration:     13,   Func. Count:    152,   Neg. LLF: 6974.854787941412\n",
            "Iteration:     14,   Func. Count:    162,   Neg. LLF: 6974.8146288351145\n",
            "Iteration:     15,   Func. Count:    172,   Neg. LLF: 6974.80897902701\n",
            "Iteration:     16,   Func. Count:    182,   Neg. LLF: 6974.806416796329\n",
            "Iteration:     17,   Func. Count:    192,   Neg. LLF: 6974.806191764981\n",
            "Iteration:     18,   Func. Count:    202,   Neg. LLF: 6974.806177130396\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6974.806177023567\n",
            "            Iterations: 18\n",
            "            Function evaluations: 202\n",
            "            Gradient evaluations: 18\n",
            "Iteration:      1,   Func. Count:     11,   Neg. LLF: 7006.622724250925\n",
            "Iteration:      2,   Func. Count:     27,   Neg. LLF: 6993.44879534354\n",
            "Iteration:      3,   Func. Count:     42,   Neg. LLF: 6992.460535857236\n",
            "Iteration:      4,   Func. Count:     56,   Neg. LLF: 6991.597908316215\n",
            "Iteration:      5,   Func. Count:     68,   Neg. LLF: 6987.092513298211\n",
            "Iteration:      6,   Func. Count:     81,   Neg. LLF: 6986.346821439418\n",
            "Iteration:      7,   Func. Count:     93,   Neg. LLF: 6983.039478181243\n",
            "Iteration:      8,   Func. Count:    105,   Neg. LLF: 6981.214887171338\n",
            "Iteration:      9,   Func. Count:    117,   Neg. LLF: 6978.9475617212065\n",
            "Iteration:     10,   Func. Count:    129,   Neg. LLF: 6977.395110711557\n",
            "Iteration:     11,   Func. Count:    141,   Neg. LLF: 6976.161677138109\n",
            "Iteration:     12,   Func. Count:    153,   Neg. LLF: 6975.725995540373\n",
            "Iteration:     13,   Func. Count:    164,   Neg. LLF: 6975.362720799288\n",
            "Iteration:     14,   Func. Count:    175,   Neg. LLF: 6974.849494305587\n",
            "Iteration:     15,   Func. Count:    186,   Neg. LLF: 6974.808996980424\n",
            "Iteration:     16,   Func. Count:    197,   Neg. LLF: 6974.807093450343\n",
            "Iteration:     17,   Func. Count:    208,   Neg. LLF: 6974.806217145404\n",
            "Iteration:     18,   Func. Count:    219,   Neg. LLF: 6974.806187194534\n",
            "Iteration:     19,   Func. Count:    230,   Neg. LLF: 6974.806176776869\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6974.806176721102\n",
            "            Iterations: 19\n",
            "            Function evaluations: 230\n",
            "            Gradient evaluations: 19\n",
            "Iteration:      1,   Func. Count:      9,   Neg. LLF: 7006.1437220817925\n",
            "Iteration:      2,   Func. Count:     24,   Neg. LLF: 6988.090981561272\n",
            "Iteration:      3,   Func. Count:     37,   Neg. LLF: 6985.3475737745375\n",
            "Iteration:      4,   Func. Count:     50,   Neg. LLF: 6985.183955234633\n",
            "Iteration:      5,   Func. Count:     62,   Neg. LLF: 6985.117347994558\n",
            "Iteration:      6,   Func. Count:     73,   Neg. LLF: 6984.636636847573\n",
            "Iteration:      7,   Func. Count:     83,   Neg. LLF: 6983.2048100942375\n",
            "Iteration:      8,   Func. Count:     93,   Neg. LLF: 6979.2012195241105\n",
            "Iteration:      9,   Func. Count:    103,   Neg. LLF: 6978.566205639404\n",
            "Iteration:     10,   Func. Count:    113,   Neg. LLF: 6977.949832988165\n",
            "Iteration:     11,   Func. Count:    122,   Neg. LLF: 6976.657108956593\n",
            "Iteration:     12,   Func. Count:    131,   Neg. LLF: 6976.068084739874\n",
            "Iteration:     13,   Func. Count:    140,   Neg. LLF: 6975.9364883779035\n",
            "Iteration:     14,   Func. Count:    149,   Neg. LLF: 6975.928779980658\n",
            "Iteration:     15,   Func. Count:    158,   Neg. LLF: 6975.927855222237\n",
            "Iteration:     16,   Func. Count:    167,   Neg. LLF: 6975.92778779123\n",
            "Iteration:     17,   Func. Count:    176,   Neg. LLF: 6975.927785297891\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6975.927785297363\n",
            "            Iterations: 17\n",
            "            Function evaluations: 176\n",
            "            Gradient evaluations: 17\n",
            "Iteration:      1,   Func. Count:     10,   Neg. LLF: 6999.955692192812\n",
            "Iteration:      2,   Func. Count:     25,   Neg. LLF: 6985.854870536337\n",
            "Iteration:      3,   Func. Count:     39,   Neg. LLF: 6985.078933336314\n",
            "Iteration:      4,   Func. Count:     52,   Neg. LLF: 6984.36442579981\n",
            "Iteration:      5,   Func. Count:     64,   Neg. LLF: 6980.175812496138\n",
            "Iteration:      6,   Func. Count:     76,   Neg. LLF: 6979.655312241215\n",
            "Iteration:      7,   Func. Count:     88,   Neg. LLF: 6979.070134752724\n",
            "Iteration:      8,   Func. Count:    100,   Neg. LLF: 6978.602798030473\n",
            "Iteration:      9,   Func. Count:    111,   Neg. LLF: 6976.524314891778\n",
            "Iteration:     10,   Func. Count:    122,   Neg. LLF: 6975.2097691240115\n",
            "Iteration:     11,   Func. Count:    133,   Neg. LLF: 6974.739264503342\n",
            "Iteration:     12,   Func. Count:    144,   Neg. LLF: 6974.487571243881\n",
            "Iteration:     13,   Func. Count:    155,   Neg. LLF: 6974.409021087942\n",
            "Iteration:     14,   Func. Count:    166,   Neg. LLF: 6974.390243962849\n",
            "Iteration:     15,   Func. Count:    177,   Neg. LLF: 6974.340252096427\n",
            "Iteration:     16,   Func. Count:    188,   Neg. LLF: 6974.330478042825\n",
            "Iteration:     17,   Func. Count:    198,   Neg. LLF: 6974.3251114410705\n",
            "Iteration:     18,   Func. Count:    208,   Neg. LLF: 6974.323718951138\n",
            "Iteration:     19,   Func. Count:    218,   Neg. LLF: 6974.32364651875\n",
            "Iteration:     20,   Func. Count:    228,   Neg. LLF: 6974.323640620861\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6974.32364062138\n",
            "            Iterations: 20\n",
            "            Function evaluations: 228\n",
            "            Gradient evaluations: 20\n",
            "Iteration:      1,   Func. Count:     11,   Neg. LLF: 7003.635119135377\n",
            "Iteration:      2,   Func. Count:     27,   Neg. LLF: 6991.622316458945\n",
            "Iteration:      3,   Func. Count:     42,   Neg. LLF: 6990.6642773808135\n",
            "Iteration:      4,   Func. Count:     55,   Neg. LLF: 6989.533728676018\n",
            "Iteration:      5,   Func. Count:     67,   Neg. LLF: 6981.652429924841\n",
            "Iteration:      6,   Func. Count:     80,   Neg. LLF: 6979.705224494597\n",
            "Iteration:      7,   Func. Count:     93,   Neg. LLF: 6978.835543304687\n",
            "Iteration:      8,   Func. Count:    105,   Neg. LLF: 6977.992265860992\n",
            "Iteration:      9,   Func. Count:    117,   Neg. LLF: 6977.812222855964\n",
            "Iteration:     10,   Func. Count:    129,   Neg. LLF: 6975.7456588917175\n",
            "Iteration:     11,   Func. Count:    141,   Neg. LLF: 6975.533477610901\n",
            "Iteration:     12,   Func. Count:    153,   Neg. LLF: 6975.0384083378485\n",
            "Iteration:     13,   Func. Count:    165,   Neg. LLF: 6974.622475237311\n",
            "Iteration:     14,   Func. Count:    177,   Neg. LLF: 6974.484897784458\n",
            "Iteration:     15,   Func. Count:    189,   Neg. LLF: 6974.39678031929\n",
            "Iteration:     16,   Func. Count:    201,   Neg. LLF: 6974.354678885879\n",
            "Iteration:     17,   Func. Count:    212,   Neg. LLF: 6974.331110681642\n",
            "Iteration:     18,   Func. Count:    223,   Neg. LLF: 6974.3248137342325\n",
            "Iteration:     19,   Func. Count:    236,   Neg. LLF: 6974.324735248561\n",
            "Iteration:     20,   Func. Count:    247,   Neg. LLF: 6974.324219409721\n",
            "Iteration:     21,   Func. Count:    258,   Neg. LLF: 6974.323863149815\n",
            "Iteration:     22,   Func. Count:    269,   Neg. LLF: 6974.323643054359\n",
            "Iteration:     23,   Func. Count:    280,   Neg. LLF: 6974.323640639004\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6974.32364063822\n",
            "            Iterations: 23\n",
            "            Function evaluations: 280\n",
            "            Gradient evaluations: 23\n",
            "Iteration:      1,   Func. Count:     12,   Neg. LLF: 7012.680063731683\n",
            "Iteration:      2,   Func. Count:     29,   Neg. LLF: 7000.241893974718\n",
            "Iteration:      3,   Func. Count:     45,   Neg. LLF: 6999.335469197245\n",
            "Iteration:      4,   Func. Count:     59,   Neg. LLF: 6998.061561319581\n",
            "Iteration:      5,   Func. Count:     72,   Neg. LLF: 6985.134969618183\n",
            "Iteration:      6,   Func. Count:     86,   Neg. LLF: 6980.4468329501\n",
            "Iteration:      7,   Func. Count:     99,   Neg. LLF: 6979.455320241909\n",
            "Iteration:      8,   Func. Count:    112,   Neg. LLF: 6977.324830613063\n",
            "Iteration:      9,   Func. Count:    125,   Neg. LLF: 6976.797688801098\n",
            "Iteration:     10,   Func. Count:    139,   Neg. LLF: 6976.739704316307\n",
            "Iteration:     11,   Func. Count:    152,   Neg. LLF: 6975.794004787232\n",
            "Iteration:     12,   Func. Count:    165,   Neg. LLF: 6974.769937079903\n",
            "Iteration:     13,   Func. Count:    178,   Neg. LLF: 6974.681913727494\n",
            "Iteration:     14,   Func. Count:    190,   Neg. LLF: 6974.417158034805\n",
            "Iteration:     15,   Func. Count:    203,   Neg. LLF: 6974.367840211843\n",
            "Iteration:     16,   Func. Count:    217,   Neg. LLF: 6974.331528072594\n",
            "Iteration:     17,   Func. Count:    229,   Neg. LLF: 6974.317115387534\n",
            "Iteration:     18,   Func. Count:    241,   Neg. LLF: 6974.315969883453\n",
            "Iteration:     19,   Func. Count:    253,   Neg. LLF: 6974.315694528686\n",
            "Iteration:     20,   Func. Count:    265,   Neg. LLF: 6974.315686495967\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6974.315686494913\n",
            "            Iterations: 20\n",
            "            Function evaluations: 265\n",
            "            Gradient evaluations: 20\n",
            "Iteration:      1,   Func. Count:     10,   Neg. LLF: 7010.445731209378\n",
            "Iteration:      2,   Func. Count:     25,   Neg. LLF: 7000.636145957154\n",
            "Iteration:      3,   Func. Count:     39,   Neg. LLF: 6997.757301597463\n",
            "Iteration:      4,   Func. Count:     53,   Neg. LLF: 6997.5205953767145\n",
            "Iteration:      5,   Func. Count:     65,   Neg. LLF: 6992.970583532496\n",
            "Iteration:      6,   Func. Count:     77,   Neg. LLF: 6988.523724209187\n",
            "Iteration:      7,   Func. Count:     88,   Neg. LLF: 6985.829734936406\n",
            "Iteration:      8,   Func. Count:     99,   Neg. LLF: 6981.598208789072\n",
            "Iteration:      9,   Func. Count:    110,   Neg. LLF: 6979.880258393463\n",
            "Iteration:     10,   Func. Count:    121,   Neg. LLF: 6979.128143528951\n",
            "Iteration:     11,   Func. Count:    132,   Neg. LLF: 6978.12832708047\n",
            "Iteration:     12,   Func. Count:    142,   Neg. LLF: 6976.487359592333\n",
            "Iteration:     13,   Func. Count:    154,   Neg. LLF: 6976.432244958833\n",
            "Iteration:     14,   Func. Count:    165,   Neg. LLF: 6976.073778666542\n",
            "Iteration:     15,   Func. Count:    176,   Neg. LLF: 6975.941225256443\n",
            "Iteration:     16,   Func. Count:    186,   Neg. LLF: 6975.929186496243\n",
            "Iteration:     17,   Func. Count:    196,   Neg. LLF: 6975.927813760719\n",
            "Iteration:     18,   Func. Count:    206,   Neg. LLF: 6975.927786084503\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6975.927785274273\n",
            "            Iterations: 18\n",
            "            Function evaluations: 207\n",
            "            Gradient evaluations: 18\n",
            "Iteration:      1,   Func. Count:     11,   Neg. LLF: 7006.568253212472\n",
            "Iteration:      2,   Func. Count:     27,   Neg. LLF: 6993.394145564953\n",
            "Iteration:      3,   Func. Count:     42,   Neg. LLF: 6992.720180030028\n",
            "Iteration:      4,   Func. Count:     56,   Neg. LLF: 6991.734139406739\n",
            "Iteration:      5,   Func. Count:     69,   Neg. LLF: 6983.994587117444\n",
            "Iteration:      6,   Func. Count:     82,   Neg. LLF: 6983.316479820317\n",
            "Iteration:      7,   Func. Count:     94,   Neg. LLF: 6979.71684934731\n",
            "Iteration:      8,   Func. Count:    107,   Neg. LLF: 6979.340306384651\n",
            "Iteration:      9,   Func. Count:    119,   Neg. LLF: 6977.395417326718\n",
            "Iteration:     10,   Func. Count:    131,   Neg. LLF: 6976.820331509707\n",
            "Iteration:     11,   Func. Count:    143,   Neg. LLF: 6975.6790779347275\n",
            "Iteration:     12,   Func. Count:    155,   Neg. LLF: 6975.091727841913\n",
            "Iteration:     13,   Func. Count:    166,   Neg. LLF: 6974.784207108115\n",
            "Iteration:     14,   Func. Count:    178,   Neg. LLF: 6974.402561118817\n",
            "Iteration:     15,   Func. Count:    191,   Neg. LLF: 6974.3903454527335\n",
            "Iteration:     16,   Func. Count:    204,   Neg. LLF: 6974.386448768288\n",
            "Iteration:     17,   Func. Count:    216,   Neg. LLF: 6974.354401497893\n",
            "Iteration:     18,   Func. Count:    227,   Neg. LLF: 6974.329794645222\n",
            "Iteration:     19,   Func. Count:    238,   Neg. LLF: 6974.323651978977\n",
            "Iteration:     20,   Func. Count:    249,   Neg. LLF: 6974.323585131485\n",
            "Iteration:     21,   Func. Count:    260,   Neg. LLF: 6974.323579340384\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6974.323579341294\n",
            "            Iterations: 21\n",
            "            Function evaluations: 260\n",
            "            Gradient evaluations: 21\n",
            "Iteration:      1,   Func. Count:     12,   Neg. LLF: 7011.394947062973\n",
            "Iteration:      2,   Func. Count:     29,   Neg. LLF: 6998.270958992467\n",
            "Iteration:      3,   Func. Count:     45,   Neg. LLF: 6997.364939867702\n",
            "Iteration:      4,   Func. Count:     59,   Neg. LLF: 6988.050953337741\n",
            "Iteration:      5,   Func. Count:     73,   Neg. LLF: 6979.125512959219\n",
            "Iteration:      6,   Func. Count:     87,   Neg. LLF: 6978.419925410375\n",
            "Iteration:      7,   Func. Count:    101,   Neg. LLF: 6977.035939772182\n",
            "Iteration:      8,   Func. Count:    115,   Neg. LLF: 6975.541996073836\n",
            "Iteration:      9,   Func. Count:    128,   Neg. LLF: 6975.090665605221\n",
            "Iteration:     10,   Func. Count:    142,   Neg. LLF: 6974.93516504061\n",
            "Iteration:     11,   Func. Count:    156,   Neg. LLF: 6974.931345273432\n",
            "Iteration:     12,   Func. Count:    170,   Neg. LLF: 6974.904354567787\n",
            "Iteration:     13,   Func. Count:    182,   Neg. LLF: 6974.197412050676\n",
            "Iteration:     14,   Func. Count:    194,   Neg. LLF: 6974.033551541587\n",
            "Iteration:     15,   Func. Count:    206,   Neg. LLF: 6974.000637715349\n",
            "Iteration:     16,   Func. Count:    218,   Neg. LLF: 6973.992296873983\n",
            "Iteration:     17,   Func. Count:    230,   Neg. LLF: 6973.991352951507\n",
            "Iteration:     18,   Func. Count:    242,   Neg. LLF: 6973.990526846893\n",
            "Iteration:     19,   Func. Count:    254,   Neg. LLF: 6973.990207655666\n",
            "Iteration:     20,   Func. Count:    266,   Neg. LLF: 6973.990128273768\n",
            "Iteration:     21,   Func. Count:    278,   Neg. LLF: 6973.9901226124675\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6973.990122613191\n",
            "            Iterations: 21\n",
            "            Function evaluations: 278\n",
            "            Gradient evaluations: 21\n",
            "Iteration:      1,   Func. Count:     13,   Neg. LLF: 7018.557433365912\n",
            "Iteration:      2,   Func. Count:     31,   Neg. LLF: 7005.963483291644\n",
            "Iteration:      3,   Func. Count:     48,   Neg. LLF: 7005.078830950412\n",
            "Iteration:      4,   Func. Count:     62,   Neg. LLF: 6993.745674920604\n",
            "Iteration:      5,   Func. Count:     76,   Neg. LLF: 6986.965405454152\n",
            "Iteration:      6,   Func. Count:     90,   Neg. LLF: 6984.739177965293\n",
            "Iteration:      7,   Func. Count:    105,   Neg. LLF: 6982.243947526143\n",
            "Iteration:      8,   Func. Count:    120,   Neg. LLF: 6980.765426593418\n",
            "Iteration:      9,   Func. Count:    135,   Neg. LLF: 6978.838191326851\n",
            "Iteration:     10,   Func. Count:    150,   Neg. LLF: 6977.276281932434\n",
            "Iteration:     11,   Func. Count:    164,   Neg. LLF: 6974.934926815993\n",
            "Iteration:     12,   Func. Count:    178,   Neg. LLF: 6974.35706066619\n",
            "Iteration:     13,   Func. Count:    192,   Neg. LLF: 6974.201880792065\n",
            "Iteration:     14,   Func. Count:    206,   Neg. LLF: 6974.06086105951\n",
            "Iteration:     15,   Func. Count:    220,   Neg. LLF: 6973.914941294177\n",
            "Iteration:     16,   Func. Count:    235,   Neg. LLF: 6973.911164711402\n",
            "Iteration:     17,   Func. Count:    249,   Neg. LLF: 6973.892795300801\n",
            "Iteration:     18,   Func. Count:    263,   Neg. LLF: 6973.872905557854\n",
            "Iteration:     19,   Func. Count:    276,   Neg. LLF: 6973.864140369724\n",
            "Iteration:     20,   Func. Count:    289,   Neg. LLF: 6973.8369457836525\n",
            "Iteration:     21,   Func. Count:    302,   Neg. LLF: 6973.815430626575\n",
            "Iteration:     22,   Func. Count:    315,   Neg. LLF: 6973.80746656199\n",
            "Iteration:     23,   Func. Count:    328,   Neg. LLF: 6973.807051441864\n",
            "Iteration:     24,   Func. Count:    341,   Neg. LLF: 6973.806970443163\n",
            "Iteration:     25,   Func. Count:    354,   Neg. LLF: 6973.806963910154\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6973.8069639096\n",
            "            Iterations: 25\n",
            "            Function evaluations: 354\n",
            "            Gradient evaluations: 25\n",
            "Iteration:      1,   Func. Count:      8,   Neg. LLF: 7021.411389321993\n",
            "Iteration:      2,   Func. Count:     21,   Neg. LLF: 7007.805669576474\n",
            "Iteration:      3,   Func. Count:     33,   Neg. LLF: 7006.402349152224\n",
            "Iteration:      4,   Func. Count:     43,   Neg. LLF: 7000.538501129163\n",
            "Iteration:      5,   Func. Count:     54,   Neg. LLF: 6995.0320625471795\n",
            "Iteration:      6,   Func. Count:     64,   Neg. LLF: 6988.232864012054\n",
            "Iteration:      7,   Func. Count:     73,   Neg. LLF: 6984.537146001944\n",
            "Iteration:      8,   Func. Count:     82,   Neg. LLF: 6981.832168275378\n",
            "Iteration:      9,   Func. Count:     91,   Neg. LLF: 6980.050211790192\n",
            "Iteration:     10,   Func. Count:    100,   Neg. LLF: 6979.168696932677\n",
            "Iteration:     11,   Func. Count:    108,   Neg. LLF: 6978.88282202715\n",
            "Iteration:     12,   Func. Count:    116,   Neg. LLF: 6978.534865543052\n",
            "Iteration:     13,   Func. Count:    124,   Neg. LLF: 6978.5254150059045\n",
            "Iteration:     14,   Func. Count:    132,   Neg. LLF: 6978.525136295938\n",
            "Iteration:     15,   Func. Count:    140,   Neg. LLF: 6978.525133211098\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6978.525133210756\n",
            "            Iterations: 15\n",
            "            Function evaluations: 140\n",
            "            Gradient evaluations: 15\n",
            "Iteration:      1,   Func. Count:      9,   Neg. LLF: 7022.84474934707\n",
            "Iteration:      2,   Func. Count:     24,   Neg. LLF: 7005.735179000852\n",
            "Iteration:      3,   Func. Count:     37,   Neg. LLF: 7003.575288513884\n",
            "Iteration:      4,   Func. Count:     50,   Neg. LLF: 7003.536703476309\n",
            "Iteration:      5,   Func. Count:     60,   Neg. LLF: 6996.6724428153175\n",
            "Iteration:      6,   Func. Count:     70,   Neg. LLF: 6993.06925334629\n",
            "Iteration:      7,   Func. Count:     80,   Neg. LLF: 6989.733122567216\n",
            "Iteration:      8,   Func. Count:     89,   Neg. LLF: 6986.951809433714\n",
            "Iteration:      9,   Func. Count:    100,   Neg. LLF: 6986.643627875803\n",
            "Iteration:     10,   Func. Count:    110,   Neg. LLF: 6980.4375505370635\n",
            "Iteration:     11,   Func. Count:    121,   Neg. LLF: 6980.295308920078\n",
            "Iteration:     12,   Func. Count:    130,   Neg. LLF: 6978.933586799287\n",
            "Iteration:     13,   Func. Count:    139,   Neg. LLF: 6978.554273504386\n",
            "Iteration:     14,   Func. Count:    149,   Neg. LLF: 6978.533128377703\n",
            "Iteration:     15,   Func. Count:    158,   Neg. LLF: 6978.525222334573\n",
            "Iteration:     16,   Func. Count:    167,   Neg. LLF: 6978.525134128015\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6978.525133126996\n",
            "            Iterations: 16\n",
            "            Function evaluations: 168\n",
            "            Gradient evaluations: 16\n",
            "Iteration:      1,   Func. Count:     10,   Neg. LLF: 7029.6202497877075\n",
            "Iteration:      2,   Func. Count:     26,   Neg. LLF: 7014.444561104972\n",
            "Iteration:      3,   Func. Count:     40,   Neg. LLF: 7013.546862422796\n",
            "Iteration:      4,   Func. Count:     53,   Neg. LLF: 7013.5063843639755\n",
            "Iteration:      5,   Func. Count:     66,   Neg. LLF: 7013.41326155911\n",
            "Iteration:      6,   Func. Count:     77,   Neg. LLF: 7005.9988631014\n",
            "Iteration:      7,   Func. Count:     88,   Neg. LLF: 6998.283466943222\n",
            "Iteration:      8,   Func. Count:     99,   Neg. LLF: 6993.789571685698\n",
            "Iteration:      9,   Func. Count:    110,   Neg. LLF: 6993.041534679898\n",
            "Iteration:     10,   Func. Count:    121,   Neg. LLF: 6989.912422777316\n",
            "Iteration:     11,   Func. Count:    131,   Neg. LLF: 6980.73375164895\n",
            "Iteration:     12,   Func. Count:    142,   Neg. LLF: 6978.976344809583\n",
            "Iteration:     13,   Func. Count:    153,   Neg. LLF: 6978.5965044282\n",
            "Iteration:     14,   Func. Count:    163,   Neg. LLF: 6978.555934007674\n",
            "Iteration:     15,   Func. Count:    173,   Neg. LLF: 6978.525261151357\n",
            "Iteration:     16,   Func. Count:    183,   Neg. LLF: 6978.525136586079\n",
            "Iteration:     17,   Func. Count:    193,   Neg. LLF: 6978.525133676823\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6978.525133134549\n",
            "            Iterations: 17\n",
            "            Function evaluations: 193\n",
            "            Gradient evaluations: 17\n",
            "Iteration:      1,   Func. Count:     11,   Neg. LLF: 7045.504720893434\n",
            "Iteration:      2,   Func. Count:     28,   Neg. LLF: 7032.1158042188545\n",
            "Iteration:      3,   Func. Count:     43,   Neg. LLF: 7030.885899832145\n",
            "Iteration:      4,   Func. Count:     58,   Neg. LLF: 7030.837452678543\n",
            "Iteration:      5,   Func. Count:     70,   Neg. LLF: 7021.481415443694\n",
            "Iteration:      6,   Func. Count:     83,   Neg. LLF: 7018.851646852214\n",
            "Iteration:      7,   Func. Count:     96,   Neg. LLF: 7018.2937543549715\n",
            "Iteration:      8,   Func. Count:    107,   Neg. LLF: 6985.601170815533\n",
            "Iteration:      9,   Func. Count:    120,   Neg. LLF: 6984.0626672859\n",
            "Iteration:     10,   Func. Count:    133,   Neg. LLF: 6981.115668292049\n",
            "Iteration:     11,   Func. Count:    144,   Neg. LLF: 6978.902684831565\n",
            "Iteration:     12,   Func. Count:    155,   Neg. LLF: 6978.559159172442\n",
            "Iteration:     13,   Func. Count:    166,   Neg. LLF: 6978.525643045847\n",
            "Iteration:     14,   Func. Count:    177,   Neg. LLF: 6978.525137417229\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6978.525136449212\n",
            "            Iterations: 14\n",
            "            Function evaluations: 179\n",
            "            Gradient evaluations: 14\n",
            "Iteration:      1,   Func. Count:      9,   Neg. LLF: 7004.541500257865\n",
            "Iteration:      2,   Func. Count:     24,   Neg. LLF: 6985.121856845432\n",
            "Iteration:      3,   Func. Count:     37,   Neg. LLF: 6982.188326947179\n",
            "Iteration:      4,   Func. Count:     50,   Neg. LLF: 6981.766573621914\n",
            "Iteration:      5,   Func. Count:     60,   Neg. LLF: 6978.068877382462\n",
            "Iteration:      6,   Func. Count:     71,   Neg. LLF: 6975.502243267129\n",
            "Iteration:      7,   Func. Count:     81,   Neg. LLF: 6973.6072709689\n",
            "Iteration:      8,   Func. Count:     91,   Neg. LLF: 6972.820421171502\n",
            "Iteration:      9,   Func. Count:    101,   Neg. LLF: 6972.709249592967\n",
            "Iteration:     10,   Func. Count:    112,   Neg. LLF: 6972.556171890797\n",
            "Iteration:     11,   Func. Count:    123,   Neg. LLF: 6972.553597640512\n",
            "Iteration:     12,   Func. Count:    134,   Neg. LLF: 6972.510361748307\n",
            "Iteration:     13,   Func. Count:    143,   Neg. LLF: 6972.5099740133755\n",
            "Iteration:     14,   Func. Count:    152,   Neg. LLF: 6972.509965349341\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6972.509965348506\n",
            "            Iterations: 14\n",
            "            Function evaluations: 152\n",
            "            Gradient evaluations: 14\n",
            "Iteration:      1,   Func. Count:     10,   Neg. LLF: 6990.574814250433\n",
            "Iteration:      2,   Func. Count:     26,   Neg. LLF: 6973.875566578081\n",
            "Iteration:      3,   Func. Count:     40,   Neg. LLF: 6972.932482429036\n",
            "Iteration:      4,   Func. Count:     53,   Neg. LLF: 6972.652239578528\n",
            "Iteration:      5,   Func. Count:     66,   Neg. LLF: 6972.514262263552\n",
            "Iteration:      6,   Func. Count:     78,   Neg. LLF: 6972.312698387343\n",
            "Iteration:      7,   Func. Count:     91,   Neg. LLF: 6972.28519784052\n",
            "Iteration:      8,   Func. Count:    102,   Neg. LLF: 6971.552337579687\n",
            "Iteration:      9,   Func. Count:    113,   Neg. LLF: 6971.4853335103835\n",
            "Iteration:     10,   Func. Count:    124,   Neg. LLF: 6971.404871231327\n",
            "Iteration:     11,   Func. Count:    135,   Neg. LLF: 6971.362161096603\n",
            "Iteration:     12,   Func. Count:    146,   Neg. LLF: 6971.337018046392\n",
            "Iteration:     13,   Func. Count:    156,   Neg. LLF: 6971.336796440886\n",
            "Iteration:     14,   Func. Count:    166,   Neg. LLF: 6971.336756716262\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6971.336756125698\n",
            "            Iterations: 14\n",
            "            Function evaluations: 167\n",
            "            Gradient evaluations: 14\n",
            "Iteration:      1,   Func. Count:     11,   Neg. LLF: 6994.283521236872\n",
            "Iteration:      2,   Func. Count:     27,   Neg. LLF: 6979.670168887058\n",
            "Iteration:      3,   Func. Count:     42,   Neg. LLF: 6978.557480343547\n",
            "Iteration:      4,   Func. Count:     56,   Neg. LLF: 6978.230998162805\n",
            "Iteration:      5,   Func. Count:     70,   Neg. LLF: 6977.7772938046155\n",
            "Iteration:      6,   Func. Count:     83,   Neg. LLF: 6975.06619165128\n",
            "Iteration:      7,   Func. Count:     96,   Neg. LLF: 6974.947070142383\n",
            "Iteration:      8,   Func. Count:    108,   Neg. LLF: 6974.260809410412\n",
            "Iteration:      9,   Func. Count:    120,   Neg. LLF: 6973.732241167146\n",
            "Iteration:     10,   Func. Count:    132,   Neg. LLF: 6972.955271833711\n",
            "Iteration:     11,   Func. Count:    144,   Neg. LLF: 6972.582577289826\n",
            "Iteration:     12,   Func. Count:    156,   Neg. LLF: 6972.096371987702\n",
            "Iteration:     13,   Func. Count:    167,   Neg. LLF: 6971.702811003357\n",
            "Iteration:     14,   Func. Count:    179,   Neg. LLF: 6971.360480102832\n",
            "Iteration:     15,   Func. Count:    190,   Neg. LLF: 6971.341055418173\n",
            "Iteration:     16,   Func. Count:    201,   Neg. LLF: 6971.337682939206\n",
            "Iteration:     17,   Func. Count:    212,   Neg. LLF: 6971.336995280901\n",
            "Iteration:     18,   Func. Count:    223,   Neg. LLF: 6971.336783426791\n",
            "Iteration:     19,   Func. Count:    234,   Neg. LLF: 6971.336757269634\n",
            "Iteration:     20,   Func. Count:    245,   Neg. LLF: 6971.33675623439\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6971.336756132809\n",
            "            Iterations: 20\n",
            "            Function evaluations: 245\n",
            "            Gradient evaluations: 20\n",
            "Iteration:      1,   Func. Count:     12,   Neg. LLF: 7004.037727679875\n",
            "Iteration:      2,   Func. Count:     29,   Neg. LLF: 6990.10219802146\n",
            "Iteration:      3,   Func. Count:     45,   Neg. LLF: 6989.0630899121\n",
            "Iteration:      4,   Func. Count:     60,   Neg. LLF: 6988.731789673768\n",
            "Iteration:      5,   Func. Count:     75,   Neg. LLF: 6988.205946908953\n",
            "Iteration:      6,   Func. Count:     88,   Neg. LLF: 6983.44719908581\n",
            "Iteration:      7,   Func. Count:    102,   Neg. LLF: 6982.713342305568\n",
            "Iteration:      8,   Func. Count:    115,   Neg. LLF: 6979.555622939419\n",
            "Iteration:      9,   Func. Count:    128,   Neg. LLF: 6977.984179478321\n",
            "Iteration:     10,   Func. Count:    141,   Neg. LLF: 6977.243092622479\n",
            "Iteration:     11,   Func. Count:    154,   Neg. LLF: 6973.647354677443\n",
            "Iteration:     12,   Func. Count:    167,   Neg. LLF: 6972.413624026136\n",
            "Iteration:     13,   Func. Count:    179,   Neg. LLF: 6972.115623690853\n",
            "Iteration:     14,   Func. Count:    192,   Neg. LLF: 6971.780896123348\n",
            "Iteration:     15,   Func. Count:    205,   Neg. LLF: 6971.4419251153695\n",
            "Iteration:     16,   Func. Count:    217,   Neg. LLF: 6971.350820614999\n",
            "Iteration:     17,   Func. Count:    229,   Neg. LLF: 6971.336894078488\n",
            "Iteration:     18,   Func. Count:    241,   Neg. LLF: 6971.336758793754\n",
            "Iteration:     19,   Func. Count:    253,   Neg. LLF: 6971.336756222199\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6971.33675618153\n",
            "            Iterations: 19\n",
            "            Function evaluations: 253\n",
            "            Gradient evaluations: 19\n",
            "Iteration:      1,   Func. Count:     10,   Neg. LLF: 7003.789875579699\n",
            "Iteration:      2,   Func. Count:     26,   Neg. LLF: 6985.060183694055\n",
            "Iteration:      3,   Func. Count:     40,   Neg. LLF: 6982.710318656957\n",
            "Iteration:      4,   Func. Count:     54,   Neg. LLF: 6982.466792434741\n",
            "Iteration:      5,   Func. Count:     67,   Neg. LLF: 6982.378703684541\n",
            "Iteration:      6,   Func. Count:     81,   Neg. LLF: 6982.364549022779\n",
            "Iteration:      7,   Func. Count:     93,   Neg. LLF: 6981.738646446039\n",
            "Iteration:      8,   Func. Count:    105,   Neg. LLF: 6980.587378128321\n",
            "Iteration:      9,   Func. Count:    116,   Neg. LLF: 6976.698482726726\n",
            "Iteration:     10,   Func. Count:    127,   Neg. LLF: 6975.880495844888\n",
            "Iteration:     11,   Func. Count:    137,   Neg. LLF: 6975.2315404158735\n",
            "Iteration:     12,   Func. Count:    147,   Neg. LLF: 6973.6412349604225\n",
            "Iteration:     13,   Func. Count:    157,   Neg. LLF: 6972.627945415956\n",
            "Iteration:     14,   Func. Count:    167,   Neg. LLF: 6972.548682039805\n",
            "Iteration:     15,   Func. Count:    177,   Neg. LLF: 6972.511171610171\n",
            "Iteration:     16,   Func. Count:    187,   Neg. LLF: 6972.510059524031\n",
            "Iteration:     17,   Func. Count:    197,   Neg. LLF: 6972.509966097479\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6972.5099652561075\n",
            "            Iterations: 17\n",
            "            Function evaluations: 198\n",
            "            Gradient evaluations: 17\n",
            "Iteration:      1,   Func. Count:     11,   Neg. LLF: 6997.480697889667\n",
            "Iteration:      2,   Func. Count:     27,   Neg. LLF: 6990.497135704361\n",
            "Iteration:      3,   Func. Count:     42,   Neg. LLF: 6989.564633881582\n",
            "Iteration:      4,   Func. Count:     56,   Neg. LLF: 6989.0751074322525\n",
            "Iteration:      5,   Func. Count:     70,   Neg. LLF: 6988.836236491023\n",
            "Iteration:      6,   Func. Count:     83,   Neg. LLF: 6976.530358179754\n",
            "Iteration:      7,   Func. Count:     96,   Neg. LLF: 6976.342821828681\n",
            "Iteration:      8,   Func. Count:    109,   Neg. LLF: 6975.866282135604\n",
            "Iteration:      9,   Func. Count:    121,   Neg. LLF: 6975.012110663949\n",
            "Iteration:     10,   Func. Count:    133,   Neg. LLF: 6972.686063675369\n",
            "Iteration:     11,   Func. Count:    145,   Neg. LLF: 6971.505082576001\n",
            "Iteration:     12,   Func. Count:    157,   Neg. LLF: 6971.250898310276\n",
            "Iteration:     13,   Func. Count:    169,   Neg. LLF: 6971.071961929003\n",
            "Iteration:     14,   Func. Count:    181,   Neg. LLF: 6970.946501572665\n",
            "Iteration:     15,   Func. Count:    193,   Neg. LLF: 6970.916766425387\n",
            "Iteration:     16,   Func. Count:    205,   Neg. LLF: 6970.880635312169\n",
            "Iteration:     17,   Func. Count:    216,   Neg. LLF: 6970.877243891569\n",
            "Iteration:     18,   Func. Count:    227,   Neg. LLF: 6970.872913874145\n",
            "Iteration:     19,   Func. Count:    238,   Neg. LLF: 6970.872609005731\n",
            "Iteration:     20,   Func. Count:    249,   Neg. LLF: 6970.872590291161\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6970.8725894220615\n",
            "            Iterations: 20\n",
            "            Function evaluations: 250\n",
            "            Gradient evaluations: 20\n",
            "Iteration:      1,   Func. Count:     12,   Neg. LLF: 7001.039393460225\n",
            "Iteration:      2,   Func. Count:     29,   Neg. LLF: 6988.253311747861\n",
            "Iteration:      3,   Func. Count:     45,   Neg. LLF: 6987.246768860662\n",
            "Iteration:      4,   Func. Count:     60,   Neg. LLF: 6986.672872983854\n",
            "Iteration:      5,   Func. Count:     75,   Neg. LLF: 6985.818100291128\n",
            "Iteration:      6,   Func. Count:     88,   Neg. LLF: 6977.2322879123385\n",
            "Iteration:      7,   Func. Count:    102,   Neg. LLF: 6975.877860338676\n",
            "Iteration:      8,   Func. Count:    116,   Neg. LLF: 6975.3153420866\n",
            "Iteration:      9,   Func. Count:    129,   Neg. LLF: 6974.104364175639\n",
            "Iteration:     10,   Func. Count:    143,   Neg. LLF: 6973.817959402824\n",
            "Iteration:     11,   Func. Count:    156,   Neg. LLF: 6972.448461777176\n",
            "Iteration:     12,   Func. Count:    170,   Neg. LLF: 6972.355591735892\n",
            "Iteration:     13,   Func. Count:    183,   Neg. LLF: 6971.658521960589\n",
            "Iteration:     14,   Func. Count:    196,   Neg. LLF: 6971.263300236342\n",
            "Iteration:     15,   Func. Count:    209,   Neg. LLF: 6970.960381065005\n",
            "Iteration:     16,   Func. Count:    222,   Neg. LLF: 6970.925471586321\n",
            "Iteration:     17,   Func. Count:    235,   Neg. LLF: 6970.885004727285\n",
            "Iteration:     18,   Func. Count:    247,   Neg. LLF: 6970.879422500582\n",
            "Iteration:     19,   Func. Count:    260,   Neg. LLF: 6970.875739188559\n",
            "Iteration:     20,   Func. Count:    273,   Neg. LLF: 6970.8715979222325\n",
            "Iteration:     21,   Func. Count:    285,   Neg. LLF: 6970.8715836364\n",
            "Iteration:     22,   Func. Count:    297,   Neg. LLF: 6970.8715791787\n",
            "Iteration:     23,   Func. Count:    309,   Neg. LLF: 6970.871575360865\n",
            "Iteration:     24,   Func. Count:    321,   Neg. LLF: 6970.871574243145\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6970.871574242456\n",
            "            Iterations: 24\n",
            "            Function evaluations: 321\n",
            "            Gradient evaluations: 24\n",
            "Iteration:      1,   Func. Count:     13,   Neg. LLF: 7009.947863652127\n",
            "Iteration:      2,   Func. Count:     31,   Neg. LLF: 6996.8038252469705\n",
            "Iteration:      3,   Func. Count:     48,   Neg. LLF: 6995.859636610797\n",
            "Iteration:      4,   Func. Count:     64,   Neg. LLF: 6995.310313745199\n",
            "Iteration:      5,   Func. Count:     79,   Neg. LLF: 6986.486917746504\n",
            "Iteration:      6,   Func. Count:     94,   Neg. LLF: 6980.280696830379\n",
            "Iteration:      7,   Func. Count:    109,   Neg. LLF: 6977.882312427838\n",
            "Iteration:      8,   Func. Count:    124,   Neg. LLF: 6975.994093890984\n",
            "Iteration:      9,   Func. Count:    138,   Neg. LLF: 6975.486766517874\n",
            "Iteration:     10,   Func. Count:    152,   Neg. LLF: 6973.673643713445\n",
            "Iteration:     11,   Func. Count:    167,   Neg. LLF: 6973.4690867332565\n",
            "Iteration:     12,   Func. Count:    182,   Neg. LLF: 6973.143277323319\n",
            "Iteration:     13,   Func. Count:    195,   Neg. LLF: 6972.539014144515\n",
            "Iteration:     14,   Func. Count:    209,   Neg. LLF: 6971.711363462322\n",
            "Iteration:     15,   Func. Count:    223,   Neg. LLF: 6971.420431954777\n",
            "Iteration:     16,   Func. Count:    238,   Neg. LLF: 6971.255223864425\n",
            "Iteration:     17,   Func. Count:    251,   Neg. LLF: 6971.012521999725\n",
            "Iteration:     18,   Func. Count:    264,   Neg. LLF: 6970.91817525885\n",
            "Iteration:     19,   Func. Count:    277,   Neg. LLF: 6970.873864107049\n",
            "Iteration:     20,   Func. Count:    290,   Neg. LLF: 6970.855690892061\n",
            "Iteration:     21,   Func. Count:    303,   Neg. LLF: 6970.852717159991\n",
            "Iteration:     22,   Func. Count:    316,   Neg. LLF: 6970.852531954895\n",
            "Iteration:     23,   Func. Count:    329,   Neg. LLF: 6970.852527550591\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6970.8525275491675\n",
            "            Iterations: 23\n",
            "            Function evaluations: 329\n",
            "            Gradient evaluations: 23\n",
            "Iteration:      1,   Func. Count:     11,   Neg. LLF: 7008.208961743501\n",
            "Iteration:      2,   Func. Count:     28,   Neg. LLF: 6989.80823566622\n",
            "Iteration:      3,   Func. Count:     43,   Neg. LLF: 6987.083180755\n",
            "Iteration:      4,   Func. Count:     58,   Neg. LLF: 6986.962893148668\n",
            "Iteration:      5,   Func. Count:     71,   Neg. LLF: 6985.3028418717\n",
            "Iteration:      6,   Func. Count:     84,   Neg. LLF: 6983.2694923161525\n",
            "Iteration:      7,   Func. Count:     97,   Neg. LLF: 6983.008373183819\n",
            "Iteration:      8,   Func. Count:    109,   Neg. LLF: 6981.366368578385\n",
            "Iteration:      9,   Func. Count:    121,   Neg. LLF: 6976.516131203005\n",
            "Iteration:     10,   Func. Count:    133,   Neg. LLF: 6975.740424016477\n",
            "Iteration:     11,   Func. Count:    145,   Neg. LLF: 6974.560121670336\n",
            "Iteration:     12,   Func. Count:    156,   Neg. LLF: 6972.844871777535\n",
            "Iteration:     13,   Func. Count:    167,   Neg. LLF: 6972.6099822044225\n",
            "Iteration:     14,   Func. Count:    178,   Neg. LLF: 6972.514703706169\n",
            "Iteration:     15,   Func. Count:    189,   Neg. LLF: 6972.512925610023\n",
            "Iteration:     16,   Func. Count:    200,   Neg. LLF: 6972.5099664334775\n",
            "Iteration:     17,   Func. Count:    211,   Neg. LLF: 6972.509965263869\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6972.509965262989\n",
            "            Iterations: 17\n",
            "            Function evaluations: 211\n",
            "            Gradient evaluations: 17\n",
            "Iteration:      1,   Func. Count:     12,   Neg. LLF: 7004.193020511573\n",
            "Iteration:      2,   Func. Count:     30,   Neg. LLF: 6988.991658684095\n",
            "Iteration:      3,   Func. Count:     46,   Neg. LLF: 6988.2916058357405\n",
            "Iteration:      4,   Func. Count:     61,   Neg. LLF: 6987.639619020902\n",
            "Iteration:      5,   Func. Count:     75,   Neg. LLF: 6984.182102232819\n",
            "Iteration:      6,   Func. Count:     89,   Neg. LLF: 6980.512939212018\n",
            "Iteration:      7,   Func. Count:    103,   Neg. LLF: 6977.164004883799\n",
            "Iteration:      8,   Func. Count:    117,   Neg. LLF: 6976.554240414545\n",
            "Iteration:      9,   Func. Count:    130,   Neg. LLF: 6974.265252407353\n",
            "Iteration:     10,   Func. Count:    143,   Neg. LLF: 6973.339091828977\n",
            "Iteration:     11,   Func. Count:    156,   Neg. LLF: 6971.746489335727\n",
            "Iteration:     12,   Func. Count:    169,   Neg. LLF: 6971.476708395294\n",
            "Iteration:     13,   Func. Count:    182,   Neg. LLF: 6971.070299558371\n",
            "Iteration:     14,   Func. Count:    195,   Neg. LLF: 6970.998150688607\n",
            "Iteration:     15,   Func. Count:    207,   Neg. LLF: 6970.925185846701\n",
            "Iteration:     16,   Func. Count:    220,   Neg. LLF: 6970.892589416178\n",
            "Iteration:     17,   Func. Count:    233,   Neg. LLF: 6970.880264750194\n",
            "Iteration:     18,   Func. Count:    245,   Neg. LLF: 6970.87395034348\n",
            "Iteration:     19,   Func. Count:    257,   Neg. LLF: 6970.872594637462\n",
            "Iteration:     20,   Func. Count:    269,   Neg. LLF: 6970.872589788825\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6970.872589787724\n",
            "            Iterations: 20\n",
            "            Function evaluations: 269\n",
            "            Gradient evaluations: 20\n",
            "Iteration:      1,   Func. Count:     13,   Neg. LLF: 7008.914224046009\n",
            "Iteration:      2,   Func. Count:     31,   Neg. LLF: 6995.100799594926\n",
            "Iteration:      3,   Func. Count:     48,   Neg. LLF: 6994.151048038447\n",
            "Iteration:      4,   Func. Count:     64,   Neg. LLF: 6993.352203842239\n",
            "Iteration:      5,   Func. Count:     79,   Neg. LLF: 6984.831300665375\n",
            "Iteration:      6,   Func. Count:     94,   Neg. LLF: 6978.985767735668\n",
            "Iteration:      7,   Func. Count:    109,   Neg. LLF: 6974.188044439572\n",
            "Iteration:      8,   Func. Count:    124,   Neg. LLF: 6972.515547837671\n",
            "Iteration:      9,   Func. Count:    139,   Neg. LLF: 6972.257835360116\n",
            "Iteration:     10,   Func. Count:    154,   Neg. LLF: 6972.181586136831\n",
            "Iteration:     11,   Func. Count:    169,   Neg. LLF: 6971.627194928796\n",
            "Iteration:     12,   Func. Count:    184,   Neg. LLF: 6971.581250553365\n",
            "Iteration:     13,   Func. Count:    198,   Neg. LLF: 6971.573073247378\n",
            "Iteration:     14,   Func. Count:    212,   Neg. LLF: 6971.397943516943\n",
            "Iteration:     15,   Func. Count:    225,   Neg. LLF: 6970.928269208127\n",
            "Iteration:     16,   Func. Count:    239,   Neg. LLF: 6970.880690206306\n",
            "Iteration:     17,   Func. Count:    252,   Neg. LLF: 6970.656734342698\n",
            "Iteration:     18,   Func. Count:    265,   Neg. LLF: 6970.636238976274\n",
            "Iteration:     19,   Func. Count:    278,   Neg. LLF: 6970.634818535259\n",
            "Iteration:     20,   Func. Count:    291,   Neg. LLF: 6970.634418029618\n",
            "Iteration:     21,   Func. Count:    304,   Neg. LLF: 6970.634406219409\n",
            "Iteration:     22,   Func. Count:    317,   Neg. LLF: 6970.634392091275\n",
            "Iteration:     23,   Func. Count:    330,   Neg. LLF: 6970.634390521296\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6970.63439052272\n",
            "            Iterations: 23\n",
            "            Function evaluations: 330\n",
            "            Gradient evaluations: 23\n",
            "Iteration:      1,   Func. Count:     14,   Neg. LLF: 7015.997002756394\n",
            "Iteration:      2,   Func. Count:     33,   Neg. LLF: 7002.723918686975\n",
            "Iteration:      3,   Func. Count:     51,   Neg. LLF: 7001.801299592424\n",
            "Iteration:      4,   Func. Count:     68,   Neg. LLF: 7000.511149667522\n",
            "Iteration:      5,   Func. Count:     83,   Neg. LLF: 6992.987717579259\n",
            "Iteration:      6,   Func. Count:     98,   Neg. LLF: 6986.824972204528\n",
            "Iteration:      7,   Func. Count:    113,   Neg. LLF: 6983.462836137878\n",
            "Iteration:      8,   Func. Count:    129,   Neg. LLF: 6979.7907023633525\n",
            "Iteration:      9,   Func. Count:    145,   Neg. LLF: 6977.807571609802\n",
            "Iteration:     10,   Func. Count:    161,   Neg. LLF: 6974.976314968465\n",
            "Iteration:     11,   Func. Count:    177,   Neg. LLF: 6974.154260974305\n",
            "Iteration:     12,   Func. Count:    192,   Neg. LLF: 6972.328269342946\n",
            "Iteration:     13,   Func. Count:    207,   Neg. LLF: 6970.915467720546\n",
            "Iteration:     14,   Func. Count:    223,   Neg. LLF: 6970.892219128395\n",
            "Iteration:     15,   Func. Count:    238,   Neg. LLF: 6970.665486950244\n",
            "Iteration:     16,   Func. Count:    253,   Neg. LLF: 6970.498734489538\n",
            "Iteration:     17,   Func. Count:    268,   Neg. LLF: 6970.467769948979\n",
            "Iteration:     18,   Func. Count:    284,   Neg. LLF: 6970.463315218964\n",
            "Iteration:     19,   Func. Count:    299,   Neg. LLF: 6970.429685097513\n",
            "Iteration:     20,   Func. Count:    313,   Neg. LLF: 6970.41847617441\n",
            "Iteration:     21,   Func. Count:    327,   Neg. LLF: 6970.412555381623\n",
            "Iteration:     22,   Func. Count:    341,   Neg. LLF: 6970.403907491034\n",
            "Iteration:     23,   Func. Count:    355,   Neg. LLF: 6970.390897857706\n",
            "Iteration:     24,   Func. Count:    369,   Neg. LLF: 6970.376501907207\n",
            "Iteration:     25,   Func. Count:    383,   Neg. LLF: 6970.362707834213\n",
            "Iteration:     26,   Func. Count:    397,   Neg. LLF: 6970.36126137338\n",
            "Iteration:     27,   Func. Count:    411,   Neg. LLF: 6970.361173525097\n",
            "Iteration:     28,   Func. Count:    425,   Neg. LLF: 6970.361164466172\n",
            "Iteration:     29,   Func. Count:    439,   Neg. LLF: 6970.361163447326\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6970.3611634474655\n",
            "            Iterations: 29\n",
            "            Function evaluations: 439\n",
            "            Gradient evaluations: 29\n",
            "Iteration:      1,   Func. Count:      9,   Neg. LLF: 7020.953766707841\n",
            "Iteration:      2,   Func. Count:     22,   Neg. LLF: 7014.318126404528\n",
            "Iteration:      3,   Func. Count:     35,   Neg. LLF: 7012.78881075962\n",
            "Iteration:      4,   Func. Count:     46,   Neg. LLF: 7002.179498938069\n",
            "Iteration:      5,   Func. Count:     58,   Neg. LLF: 7000.064072527715\n",
            "Iteration:      6,   Func. Count:     69,   Neg. LLF: 6993.225755478663\n",
            "Iteration:      7,   Func. Count:     81,   Neg. LLF: 6988.154904943409\n",
            "Iteration:      8,   Func. Count:     91,   Neg. LLF: 6982.245252244074\n",
            "Iteration:      9,   Func. Count:    103,   Neg. LLF: 6981.872096051776\n",
            "Iteration:     10,   Func. Count:    113,   Neg. LLF: 6978.016100781458\n",
            "Iteration:     11,   Func. Count:    124,   Neg. LLF: 6977.478609688322\n",
            "Iteration:     12,   Func. Count:    134,   Neg. LLF: 6977.229444200578\n",
            "Iteration:     13,   Func. Count:    143,   Neg. LLF: 6976.639869093658\n",
            "Iteration:     14,   Func. Count:    152,   Neg. LLF: 6976.580462021277\n",
            "Iteration:     15,   Func. Count:    161,   Neg. LLF: 6976.580255017268\n",
            "Iteration:     16,   Func. Count:    170,   Neg. LLF: 6976.580252558815\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6976.580252559173\n",
            "            Iterations: 16\n",
            "            Function evaluations: 170\n",
            "            Gradient evaluations: 16\n",
            "Iteration:      1,   Func. Count:     10,   Neg. LLF: 7022.299508017508\n",
            "Iteration:      2,   Func. Count:     26,   Neg. LLF: 7003.727220747459\n",
            "Iteration:      3,   Func. Count:     40,   Neg. LLF: 7001.31239099467\n",
            "Iteration:      4,   Func. Count:     54,   Neg. LLF: 7001.268183520621\n",
            "Iteration:      5,   Func. Count:     65,   Neg. LLF: 7000.373824742279\n",
            "Iteration:      6,   Func. Count:     76,   Neg. LLF: 6993.2363356141195\n",
            "Iteration:      7,   Func. Count:     88,   Neg. LLF: 6990.328785494217\n",
            "Iteration:      8,   Func. Count:     99,   Neg. LLF: 6988.306315917227\n",
            "Iteration:      9,   Func. Count:    110,   Neg. LLF: 6986.818787548249\n",
            "Iteration:     10,   Func. Count:    121,   Neg. LLF: 6983.679465800226\n",
            "Iteration:     11,   Func. Count:    134,   Neg. LLF: 6982.995186440217\n",
            "Iteration:     12,   Func. Count:    144,   Neg. LLF: 6977.1866119425695\n",
            "Iteration:     13,   Func. Count:    155,   Neg. LLF: 6976.825743881796\n",
            "Iteration:     14,   Func. Count:    166,   Neg. LLF: 6976.595209474115\n",
            "Iteration:     15,   Func. Count:    176,   Neg. LLF: 6976.582941949693\n",
            "Iteration:     16,   Func. Count:    186,   Neg. LLF: 6976.580262860988\n",
            "Iteration:     17,   Func. Count:    196,   Neg. LLF: 6976.580253482127\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6976.58025267037\n",
            "            Iterations: 17\n",
            "            Function evaluations: 197\n",
            "            Gradient evaluations: 17\n",
            "Iteration:      1,   Func. Count:     11,   Neg. LLF: 7029.155646731353\n",
            "Iteration:      2,   Func. Count:     28,   Neg. LLF: 7012.457159389711\n",
            "Iteration:      3,   Func. Count:     43,   Neg. LLF: 7011.21988500788\n",
            "Iteration:      4,   Func. Count:     58,   Neg. LLF: 7011.151686400559\n",
            "Iteration:      5,   Func. Count:     72,   Neg. LLF: 7011.076571508584\n",
            "Iteration:      6,   Func. Count:     86,   Neg. LLF: 7010.929365673062\n",
            "Iteration:      7,   Func. Count:     98,   Neg. LLF: 7003.660684362316\n",
            "Iteration:      8,   Func. Count:    110,   Neg. LLF: 6995.7887550283995\n",
            "Iteration:      9,   Func. Count:    122,   Neg. LLF: 6991.389649568338\n",
            "Iteration:     10,   Func. Count:    135,   Neg. LLF: 6990.699304221769\n",
            "Iteration:     11,   Func. Count:    147,   Neg. LLF: 6989.073242067164\n",
            "Iteration:     12,   Func. Count:    158,   Neg. LLF: 6978.2398394031325\n",
            "Iteration:     13,   Func. Count:    170,   Neg. LLF: 6976.818586077294\n",
            "Iteration:     14,   Func. Count:    182,   Neg. LLF: 6976.60935589297\n",
            "Iteration:     15,   Func. Count:    194,   Neg. LLF: 6976.581041704996\n",
            "Iteration:     16,   Func. Count:    205,   Neg. LLF: 6976.580392855546\n",
            "Iteration:     17,   Func. Count:    216,   Neg. LLF: 6976.580256478757\n",
            "Iteration:     18,   Func. Count:    227,   Neg. LLF: 6976.580253098042\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6976.580252569115\n",
            "            Iterations: 18\n",
            "            Function evaluations: 227\n",
            "            Gradient evaluations: 18\n",
            "Iteration:      1,   Func. Count:     12,   Neg. LLF: 7045.053468333442\n",
            "Iteration:      2,   Func. Count:     30,   Neg. LLF: 7030.0607305304475\n",
            "Iteration:      3,   Func. Count:     46,   Neg. LLF: 7028.570979186081\n",
            "Iteration:      4,   Func. Count:     62,   Neg. LLF: 7028.507035371596\n",
            "Iteration:      5,   Func. Count:     76,   Neg. LLF: 7026.594929932065\n",
            "Iteration:      6,   Func. Count:     89,   Neg. LLF: 7017.590531015443\n",
            "Iteration:      7,   Func. Count:    103,   Neg. LLF: 7015.372251180572\n",
            "Iteration:      8,   Func. Count:    117,   Neg. LLF: 7014.45048467243\n",
            "Iteration:      9,   Func. Count:    130,   Neg. LLF: 6998.7375464681945\n",
            "Iteration:     10,   Func. Count:    143,   Neg. LLF: 6996.744515197168\n",
            "Iteration:     11,   Func. Count:    156,   Neg. LLF: 6994.5613034761345\n",
            "Iteration:     12,   Func. Count:    169,   Neg. LLF: 6993.459232777414\n",
            "Iteration:     13,   Func. Count:    181,   Neg. LLF: 6980.899026000518\n",
            "Iteration:     14,   Func. Count:    194,   Neg. LLF: 6977.976524353721\n",
            "Iteration:     15,   Func. Count:    207,   Neg. LLF: 6977.277275436403\n",
            "Iteration:     16,   Func. Count:    219,   Neg. LLF: 6976.73377295784\n",
            "Iteration:     17,   Func. Count:    231,   Neg. LLF: 6976.586462529183\n",
            "Iteration:     18,   Func. Count:    243,   Neg. LLF: 6976.580347012405\n",
            "Iteration:     19,   Func. Count:    255,   Neg. LLF: 6976.580253979192\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6976.580252555943\n",
            "            Iterations: 19\n",
            "            Function evaluations: 256\n",
            "            Gradient evaluations: 19\n",
            "Iteration:      1,   Func. Count:     10,   Neg. LLF: 7004.063093781714\n",
            "Iteration:      2,   Func. Count:     26,   Neg. LLF: 6982.887508105065\n",
            "Iteration:      3,   Func. Count:     41,   Neg. LLF: 6978.715644919115\n",
            "Iteration:      4,   Func. Count:     55,   Neg. LLF: 6978.305743177525\n",
            "Iteration:      5,   Func. Count:     68,   Neg. LLF: 6978.2333567479045\n",
            "Iteration:      6,   Func. Count:     79,   Neg. LLF: 6974.612571777351\n",
            "Iteration:      7,   Func. Count:     90,   Neg. LLF: 6972.294883307223\n",
            "Iteration:      8,   Func. Count:    102,   Neg. LLF: 6971.856634177095\n",
            "Iteration:      9,   Func. Count:    115,   Neg. LLF: 6971.843397885388\n",
            "Iteration:     10,   Func. Count:    128,   Neg. LLF: 6971.484046562979\n",
            "Iteration:     11,   Func. Count:    139,   Neg. LLF: 6971.028280065646\n",
            "Iteration:     12,   Func. Count:    150,   Neg. LLF: 6970.866535171878\n",
            "Iteration:     13,   Func. Count:    160,   Neg. LLF: 6970.774568733648\n",
            "Iteration:     14,   Func. Count:    171,   Neg. LLF: 6970.773406447828\n",
            "Iteration:     15,   Func. Count:    181,   Neg. LLF: 6970.773331941342\n",
            "Iteration:     16,   Func. Count:    191,   Neg. LLF: 6970.773315558887\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6970.773315557217\n",
            "            Iterations: 16\n",
            "            Function evaluations: 191\n",
            "            Gradient evaluations: 16\n",
            "Iteration:      1,   Func. Count:     11,   Neg. LLF: 6990.054035332214\n",
            "Iteration:      2,   Func. Count:     28,   Neg. LLF: 6972.380719791999\n",
            "Iteration:      3,   Func. Count:     43,   Neg. LLF: 6971.1390446082805\n",
            "Iteration:      4,   Func. Count:     57,   Neg. LLF: 6970.780794217482\n",
            "Iteration:      5,   Func. Count:     71,   Neg. LLF: 6970.72663835361\n",
            "Iteration:      6,   Func. Count:     84,   Neg. LLF: 6970.531305635668\n",
            "Iteration:      7,   Func. Count:     98,   Neg. LLF: 6970.505295087734\n",
            "Iteration:      8,   Func. Count:    111,   Neg. LLF: 6970.494839389665\n",
            "Iteration:      9,   Func. Count:    123,   Neg. LLF: 6969.795824025757\n",
            "Iteration:     10,   Func. Count:    135,   Neg. LLF: 6969.748883325143\n",
            "Iteration:     11,   Func. Count:    147,   Neg. LLF: 6969.69522201176\n",
            "Iteration:     12,   Func. Count:    159,   Neg. LLF: 6969.646656867283\n",
            "Iteration:     13,   Func. Count:    170,   Neg. LLF: 6969.632447032923\n",
            "Iteration:     14,   Func. Count:    181,   Neg. LLF: 6969.628117772127\n",
            "Iteration:     15,   Func. Count:    192,   Neg. LLF: 6969.627539927587\n",
            "Iteration:     16,   Func. Count:    203,   Neg. LLF: 6969.627506911055\n",
            "Iteration:     17,   Func. Count:    214,   Neg. LLF: 6969.627505739783\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6969.627505739776\n",
            "            Iterations: 17\n",
            "            Function evaluations: 214\n",
            "            Gradient evaluations: 17\n",
            "Iteration:      1,   Func. Count:     12,   Neg. LLF: 6993.767079244693\n",
            "Iteration:      2,   Func. Count:     29,   Neg. LLF: 6978.174648520111\n",
            "Iteration:      3,   Func. Count:     45,   Neg. LLF: 6976.84017613228\n",
            "Iteration:      4,   Func. Count:     60,   Neg. LLF: 6976.387040719206\n",
            "Iteration:      5,   Func. Count:     75,   Neg. LLF: 6975.999341389482\n",
            "Iteration:      6,   Func. Count:     89,   Neg. LLF: 6975.464820768241\n",
            "Iteration:      7,   Func. Count:    103,   Neg. LLF: 6973.317118033558\n",
            "Iteration:      8,   Func. Count:    118,   Neg. LLF: 6973.042247066305\n",
            "Iteration:      9,   Func. Count:    131,   Neg. LLF: 6972.470419947062\n",
            "Iteration:     10,   Func. Count:    144,   Neg. LLF: 6972.107172214792\n",
            "Iteration:     11,   Func. Count:    157,   Neg. LLF: 6971.837678540907\n",
            "Iteration:     12,   Func. Count:    169,   Neg. LLF: 6970.382185590308\n",
            "Iteration:     13,   Func. Count:    182,   Neg. LLF: 6970.1083641064615\n",
            "Iteration:     14,   Func. Count:    195,   Neg. LLF: 6969.838216197159\n",
            "Iteration:     15,   Func. Count:    207,   Neg. LLF: 6969.630707841069\n",
            "Iteration:     16,   Func. Count:    219,   Neg. LLF: 6969.628189208058\n",
            "Iteration:     17,   Func. Count:    231,   Neg. LLF: 6969.627666003547\n",
            "Iteration:     18,   Func. Count:    243,   Neg. LLF: 6969.62751558425\n",
            "Iteration:     19,   Func. Count:    255,   Neg. LLF: 6969.627506339424\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6969.627505752962\n",
            "            Iterations: 19\n",
            "            Function evaluations: 256\n",
            "            Gradient evaluations: 19\n",
            "Iteration:      1,   Func. Count:     13,   Neg. LLF: 7003.527669991599\n",
            "Iteration:      2,   Func. Count:     31,   Neg. LLF: 6988.507537772898\n",
            "Iteration:      3,   Func. Count:     48,   Neg. LLF: 6987.303297157905\n",
            "Iteration:      4,   Func. Count:     64,   Neg. LLF: 6986.929152083048\n",
            "Iteration:      5,   Func. Count:     80,   Neg. LLF: 6986.426027118873\n",
            "Iteration:      6,   Func. Count:     95,   Neg. LLF: 6985.856261922785\n",
            "Iteration:      7,   Func. Count:    109,   Neg. LLF: 6982.901007319546\n",
            "Iteration:      8,   Func. Count:    124,   Neg. LLF: 6982.080167200182\n",
            "Iteration:      9,   Func. Count:    138,   Neg. LLF: 6979.416100901377\n",
            "Iteration:     10,   Func. Count:    152,   Neg. LLF: 6977.310773480198\n",
            "Iteration:     11,   Func. Count:    167,   Neg. LLF: 6975.4015549797705\n",
            "Iteration:     12,   Func. Count:    181,   Neg. LLF: 6971.63641629684\n",
            "Iteration:     13,   Func. Count:    195,   Neg. LLF: 6971.093501899076\n",
            "Iteration:     14,   Func. Count:    209,   Neg. LLF: 6970.71877461223\n",
            "Iteration:     15,   Func. Count:    223,   Neg. LLF: 6970.324379631374\n",
            "Iteration:     16,   Func. Count:    236,   Neg. LLF: 6969.737839391417\n",
            "Iteration:     17,   Func. Count:    249,   Neg. LLF: 6969.632483390567\n",
            "Iteration:     18,   Func. Count:    262,   Neg. LLF: 6969.628012414359\n",
            "Iteration:     19,   Func. Count:    275,   Neg. LLF: 6969.627528779235\n",
            "Iteration:     20,   Func. Count:    288,   Neg. LLF: 6969.627507670029\n",
            "Iteration:     21,   Func. Count:    301,   Neg. LLF: 6969.627505810847\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6969.627505775667\n",
            "            Iterations: 21\n",
            "            Function evaluations: 301\n",
            "            Gradient evaluations: 21\n",
            "Iteration:      1,   Func. Count:     11,   Neg. LLF: 7003.273098458494\n",
            "Iteration:      2,   Func. Count:     28,   Neg. LLF: 6983.540032509862\n",
            "Iteration:      3,   Func. Count:     43,   Neg. LLF: 6981.862945329825\n",
            "Iteration:      4,   Func. Count:     58,   Neg. LLF: 6981.555320383745\n",
            "Iteration:      5,   Func. Count:     72,   Neg. LLF: 6981.506526653641\n",
            "Iteration:      6,   Func. Count:     86,   Neg. LLF: 6981.419116363884\n",
            "Iteration:      7,   Func. Count:    100,   Neg. LLF: 6981.359257330741\n",
            "Iteration:      8,   Func. Count:    112,   Neg. LLF: 6978.825379316193\n",
            "Iteration:      9,   Func. Count:    124,   Neg. LLF: 6977.0603240380005\n",
            "Iteration:     10,   Func. Count:    137,   Neg. LLF: 6976.915219938961\n",
            "Iteration:     11,   Func. Count:    149,   Neg. LLF: 6973.964780109485\n",
            "Iteration:     12,   Func. Count:    161,   Neg. LLF: 6973.145809410373\n",
            "Iteration:     13,   Func. Count:    173,   Neg. LLF: 6972.593480836721\n",
            "Iteration:     14,   Func. Count:    184,   Neg. LLF: 6970.884441841822\n",
            "Iteration:     15,   Func. Count:    195,   Neg. LLF: 6970.784507118635\n",
            "Iteration:     16,   Func. Count:    206,   Neg. LLF: 6970.777067357659\n",
            "Iteration:     17,   Func. Count:    217,   Neg. LLF: 6970.774712530597\n",
            "Iteration:     18,   Func. Count:    228,   Neg. LLF: 6970.773338983892\n",
            "Iteration:     19,   Func. Count:    239,   Neg. LLF: 6970.773315845882\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6970.773315197991\n",
            "            Iterations: 19\n",
            "            Function evaluations: 240\n",
            "            Gradient evaluations: 19\n",
            "Iteration:      1,   Func. Count:     12,   Neg. LLF: 6996.929900230486\n",
            "Iteration:      2,   Func. Count:     29,   Neg. LLF: 6981.149174142366\n",
            "Iteration:      3,   Func. Count:     45,   Neg. LLF: 6980.083888883192\n",
            "Iteration:      4,   Func. Count:     60,   Neg. LLF: 6979.503964564605\n",
            "Iteration:      5,   Func. Count:     75,   Neg. LLF: 6979.298403023966\n",
            "Iteration:      6,   Func. Count:     89,   Neg. LLF: 6977.020854284356\n",
            "Iteration:      7,   Func. Count:    103,   Neg. LLF: 6975.050779145597\n",
            "Iteration:      8,   Func. Count:    117,   Neg. LLF: 6974.563565340855\n",
            "Iteration:      9,   Func. Count:    131,   Neg. LLF: 6973.901859754716\n",
            "Iteration:     10,   Func. Count:    145,   Neg. LLF: 6973.30136092119\n",
            "Iteration:     11,   Func. Count:    158,   Neg. LLF: 6971.771650015153\n",
            "Iteration:     12,   Func. Count:    171,   Neg. LLF: 6970.138281292898\n",
            "Iteration:     13,   Func. Count:    184,   Neg. LLF: 6969.635752668841\n",
            "Iteration:     14,   Func. Count:    197,   Neg. LLF: 6969.379926613417\n",
            "Iteration:     15,   Func. Count:    210,   Neg. LLF: 6969.256264060241\n",
            "Iteration:     16,   Func. Count:    223,   Neg. LLF: 6969.223389575047\n",
            "Iteration:     17,   Func. Count:    237,   Neg. LLF: 6969.208553533531\n",
            "Iteration:     18,   Func. Count:    250,   Neg. LLF: 6969.193339434285\n",
            "Iteration:     19,   Func. Count:    262,   Neg. LLF: 6969.192588105242\n",
            "Iteration:     20,   Func. Count:    274,   Neg. LLF: 6969.192481462252\n",
            "Iteration:     21,   Func. Count:    286,   Neg. LLF: 6969.192468883777\n",
            "Iteration:     22,   Func. Count:    298,   Neg. LLF: 6969.192467678736\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6969.192467678722\n",
            "            Iterations: 22\n",
            "            Function evaluations: 298\n",
            "            Gradient evaluations: 22\n",
            "Iteration:      1,   Func. Count:     13,   Neg. LLF: 7000.518245323588\n",
            "Iteration:      2,   Func. Count:     31,   Neg. LLF: 6986.261037843743\n",
            "Iteration:      3,   Func. Count:     48,   Neg. LLF: 6985.064642921814\n",
            "Iteration:      4,   Func. Count:     63,   Neg. LLF: 6984.5034292818655\n",
            "Iteration:      5,   Func. Count:     79,   Neg. LLF: 6984.214084396287\n",
            "Iteration:      6,   Func. Count:     93,   Neg. LLF: 6976.733612442854\n",
            "Iteration:      7,   Func. Count:    109,   Neg. LLF: 6976.456092122666\n",
            "Iteration:      8,   Func. Count:    124,   Neg. LLF: 6975.172247954127\n",
            "Iteration:      9,   Func. Count:    139,   Neg. LLF: 6974.441643443432\n",
            "Iteration:     10,   Func. Count:    153,   Neg. LLF: 6973.03832323483\n",
            "Iteration:     11,   Func. Count:    167,   Neg. LLF: 6971.978718465611\n",
            "Iteration:     12,   Func. Count:    181,   Neg. LLF: 6970.33237353912\n",
            "Iteration:     13,   Func. Count:    195,   Neg. LLF: 6970.18673922971\n",
            "Iteration:     14,   Func. Count:    209,   Neg. LLF: 6969.848219267397\n",
            "Iteration:     15,   Func. Count:    223,   Neg. LLF: 6969.49222956704\n",
            "Iteration:     16,   Func. Count:    237,   Neg. LLF: 6969.361523644399\n",
            "Iteration:     17,   Func. Count:    251,   Neg. LLF: 6969.257630465272\n",
            "Iteration:     18,   Func. Count:    265,   Neg. LLF: 6969.2052041363695\n",
            "Iteration:     19,   Func. Count:    279,   Neg. LLF: 6969.196551357058\n",
            "Iteration:     20,   Func. Count:    292,   Neg. LLF: 6969.194080115245\n",
            "Iteration:     21,   Func. Count:    305,   Neg. LLF: 6969.191878382715\n",
            "Iteration:     22,   Func. Count:    318,   Neg. LLF: 6969.191633186863\n",
            "Iteration:     23,   Func. Count:    331,   Neg. LLF: 6969.191507543519\n",
            "Iteration:     24,   Func. Count:    344,   Neg. LLF: 6969.191420244084\n",
            "Iteration:     25,   Func. Count:    357,   Neg. LLF: 6969.191419239154\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6969.191419240509\n",
            "            Iterations: 25\n",
            "            Function evaluations: 357\n",
            "            Gradient evaluations: 25\n",
            "Iteration:      1,   Func. Count:     14,   Neg. LLF: 7009.437908575785\n",
            "Iteration:      2,   Func. Count:     33,   Neg. LLF: 6995.26093009333\n",
            "Iteration:      3,   Func. Count:     51,   Neg. LLF: 6994.153720441222\n",
            "Iteration:      4,   Func. Count:     67,   Neg. LLF: 6993.500093137218\n",
            "Iteration:      5,   Func. Count:     83,   Neg. LLF: 6988.129608392892\n",
            "Iteration:      6,   Func. Count:     99,   Neg. LLF: 6980.641212994113\n",
            "Iteration:      7,   Func. Count:    116,   Neg. LLF: 6977.49947444877\n",
            "Iteration:      8,   Func. Count:    132,   Neg. LLF: 6975.353537015457\n",
            "Iteration:      9,   Func. Count:    148,   Neg. LLF: 6974.277945496353\n",
            "Iteration:     10,   Func. Count:    163,   Neg. LLF: 6973.2675142687185\n",
            "Iteration:     11,   Func. Count:    178,   Neg. LLF: 6972.264490890665\n",
            "Iteration:     12,   Func. Count:    194,   Neg. LLF: 6971.994910447078\n",
            "Iteration:     13,   Func. Count:    209,   Neg. LLF: 6970.605292120392\n",
            "Iteration:     14,   Func. Count:    224,   Neg. LLF: 6969.505803830856\n",
            "Iteration:     15,   Func. Count:    239,   Neg. LLF: 6969.4101572499985\n",
            "Iteration:     16,   Func. Count:    254,   Neg. LLF: 6969.316890899732\n",
            "Iteration:     17,   Func. Count:    269,   Neg. LLF: 6969.2976094392725\n",
            "Iteration:     18,   Func. Count:    284,   Neg. LLF: 6969.193931713331\n",
            "Iteration:     19,   Func. Count:    298,   Neg. LLF: 6969.168584266089\n",
            "Iteration:     20,   Func. Count:    312,   Neg. LLF: 6969.1676770428485\n",
            "Iteration:     21,   Func. Count:    326,   Neg. LLF: 6969.167302052992\n",
            "Iteration:     22,   Func. Count:    340,   Neg. LLF: 6969.167299590198\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6969.167299589727\n",
            "            Iterations: 22\n",
            "            Function evaluations: 340\n",
            "            Gradient evaluations: 22\n",
            "Iteration:      1,   Func. Count:     12,   Neg. LLF: 7007.638109755295\n",
            "Iteration:      2,   Func. Count:     30,   Neg. LLF: 6988.50087722696\n",
            "Iteration:      3,   Func. Count:     46,   Neg. LLF: 6985.6634824722605\n",
            "Iteration:      4,   Func. Count:     62,   Neg. LLF: 6985.495145763294\n",
            "Iteration:      5,   Func. Count:     77,   Neg. LLF: 6984.79149533259\n",
            "Iteration:      6,   Func. Count:     91,   Neg. LLF: 6981.778964389861\n",
            "Iteration:      7,   Func. Count:    107,   Neg. LLF: 6981.704428537807\n",
            "Iteration:      8,   Func. Count:    121,   Neg. LLF: 6981.405282838572\n",
            "Iteration:      9,   Func. Count:    134,   Neg. LLF: 6979.8852855271825\n",
            "Iteration:     10,   Func. Count:    146,   Neg. LLF: 6978.024014268527\n",
            "Iteration:     11,   Func. Count:    159,   Neg. LLF: 6976.864950241082\n",
            "Iteration:     12,   Func. Count:    172,   Neg. LLF: 6972.576287976318\n",
            "Iteration:     13,   Func. Count:    185,   Neg. LLF: 6970.834117895286\n",
            "Iteration:     14,   Func. Count:    197,   Neg. LLF: 6970.801310849083\n",
            "Iteration:     15,   Func. Count:    210,   Neg. LLF: 6970.778067466857\n",
            "Iteration:     16,   Func. Count:    222,   Neg. LLF: 6970.7747959701355\n",
            "Iteration:     17,   Func. Count:    234,   Neg. LLF: 6970.773322695087\n",
            "Iteration:     18,   Func. Count:    246,   Neg. LLF: 6970.773315604905\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6970.773315604648\n",
            "            Iterations: 18\n",
            "            Function evaluations: 246\n",
            "            Gradient evaluations: 18\n",
            "Iteration:      1,   Func. Count:     13,   Neg. LLF: 7003.642281096795\n",
            "Iteration:      2,   Func. Count:     31,   Neg. LLF: 6992.473297187003\n",
            "Iteration:      3,   Func. Count:     48,   Neg. LLF: 6991.568190173482\n",
            "Iteration:      4,   Func. Count:     63,   Neg. LLF: 6988.657893914044\n",
            "Iteration:      5,   Func. Count:     78,   Neg. LLF: 6985.392601123051\n",
            "Iteration:      6,   Func. Count:     94,   Neg. LLF: 6984.269082948607\n",
            "Iteration:      7,   Func. Count:    110,   Neg. LLF: 6979.537257128429\n",
            "Iteration:      8,   Func. Count:    125,   Neg. LLF: 6976.0467135545805\n",
            "Iteration:      9,   Func. Count:    140,   Neg. LLF: 6975.192089012709\n",
            "Iteration:     10,   Func. Count:    155,   Neg. LLF: 6974.179393765513\n",
            "Iteration:     11,   Func. Count:    169,   Neg. LLF: 6972.596538209019\n",
            "Iteration:     12,   Func. Count:    183,   Neg. LLF: 6971.486652369316\n",
            "Iteration:     13,   Func. Count:    197,   Neg. LLF: 6970.673490882941\n",
            "Iteration:     14,   Func. Count:    211,   Neg. LLF: 6970.081248242892\n",
            "Iteration:     15,   Func. Count:    225,   Neg. LLF: 6969.814918699901\n",
            "Iteration:     16,   Func. Count:    239,   Neg. LLF: 6969.547261457183\n",
            "Iteration:     17,   Func. Count:    253,   Neg. LLF: 6969.305160660351\n",
            "Iteration:     18,   Func. Count:    267,   Neg. LLF: 6969.25472058548\n",
            "Iteration:     19,   Func. Count:    280,   Neg. LLF: 6969.212996870518\n",
            "Iteration:     20,   Func. Count:    293,   Neg. LLF: 6969.202240792504\n",
            "Iteration:     21,   Func. Count:    307,   Neg. LLF: 6969.19580765911\n",
            "Iteration:     22,   Func. Count:    320,   Neg. LLF: 6969.1945361592\n",
            "Iteration:     23,   Func. Count:    333,   Neg. LLF: 6969.192470037991\n",
            "Iteration:     24,   Func. Count:    346,   Neg. LLF: 6969.192467682992\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6969.192467683295\n",
            "            Iterations: 24\n",
            "            Function evaluations: 346\n",
            "            Gradient evaluations: 24\n",
            "Iteration:      1,   Func. Count:     14,   Neg. LLF: 7008.411751905265\n",
            "Iteration:      2,   Func. Count:     33,   Neg. LLF: 6993.723667075848\n",
            "Iteration:      3,   Func. Count:     51,   Neg. LLF: 6992.66634835775\n",
            "Iteration:      4,   Func. Count:     67,   Neg. LLF: 6988.969664419208\n",
            "Iteration:      5,   Func. Count:     83,   Neg. LLF: 6982.713744288545\n",
            "Iteration:      6,   Func. Count:     99,   Neg. LLF: 6977.466485622421\n",
            "Iteration:      7,   Func. Count:    117,   Neg. LLF: 6977.012871791658\n",
            "Iteration:      8,   Func. Count:    133,   Neg. LLF: 6972.353269608109\n",
            "Iteration:      9,   Func. Count:    149,   Neg. LLF: 6970.872731636657\n",
            "Iteration:     10,   Func. Count:    164,   Neg. LLF: 6970.500009853595\n",
            "Iteration:     11,   Func. Count:    180,   Neg. LLF: 6970.298058017734\n",
            "Iteration:     12,   Func. Count:    196,   Neg. LLF: 6970.135617847797\n",
            "Iteration:     13,   Func. Count:    212,   Neg. LLF: 6970.034518298134\n",
            "Iteration:     14,   Func. Count:    227,   Neg. LLF: 6969.892211768582\n",
            "Iteration:     15,   Func. Count:    243,   Neg. LLF: 6969.808549822349\n",
            "Iteration:     16,   Func. Count:    257,   Neg. LLF: 6969.171396015154\n",
            "Iteration:     17,   Func. Count:    271,   Neg. LLF: 6969.066706176107\n",
            "Iteration:     18,   Func. Count:    285,   Neg. LLF: 6969.033814434657\n",
            "Iteration:     19,   Func. Count:    299,   Neg. LLF: 6968.9980325304405\n",
            "Iteration:     20,   Func. Count:    313,   Neg. LLF: 6968.981087213645\n",
            "Iteration:     21,   Func. Count:    327,   Neg. LLF: 6968.977213428298\n",
            "Iteration:     22,   Func. Count:    341,   Neg. LLF: 6968.976938314256\n",
            "Iteration:     23,   Func. Count:    355,   Neg. LLF: 6968.976917851982\n",
            "Iteration:     24,   Func. Count:    369,   Neg. LLF: 6968.976914659479\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6968.976914659363\n",
            "            Iterations: 24\n",
            "            Function evaluations: 369\n",
            "            Gradient evaluations: 24\n",
            "Iteration:      1,   Func. Count:     15,   Neg. LLF: 7015.529315697002\n",
            "Iteration:      2,   Func. Count:     35,   Neg. LLF: 7001.289218931544\n",
            "Iteration:      3,   Func. Count:     54,   Neg. LLF: 7000.275961243389\n",
            "Iteration:      4,   Func. Count:     71,   Neg. LLF: 6993.853617008897\n",
            "Iteration:      5,   Func. Count:     88,   Neg. LLF: 6984.463399245969\n",
            "Iteration:      6,   Func. Count:    106,   Neg. LLF: 6983.860612522339\n",
            "Iteration:      7,   Func. Count:    123,   Neg. LLF: 6976.473594092036\n",
            "Iteration:      8,   Func. Count:    140,   Neg. LLF: 6973.278177841808\n",
            "Iteration:      9,   Func. Count:    157,   Neg. LLF: 6969.945962690699\n",
            "Iteration:     10,   Func. Count:    174,   Neg. LLF: 6969.619653482376\n",
            "Iteration:     11,   Func. Count:    191,   Neg. LLF: 6969.235372200513\n",
            "Iteration:     12,   Func. Count:    209,   Neg. LLF: 6969.210171623239\n",
            "Iteration:     13,   Func. Count:    226,   Neg. LLF: 6969.152702063391\n",
            "Iteration:     14,   Func. Count:    242,   Neg. LLF: 6969.074005841575\n",
            "Iteration:     15,   Func. Count:    258,   Neg. LLF: 6968.818339697085\n",
            "Iteration:     16,   Func. Count:    275,   Neg. LLF: 6968.805782610434\n",
            "Iteration:     17,   Func. Count:    291,   Neg. LLF: 6968.726737911329\n",
            "Iteration:     18,   Func. Count:    307,   Neg. LLF: 6968.723162878394\n",
            "Iteration:     19,   Func. Count:    323,   Neg. LLF: 6968.717479916806\n",
            "Iteration:     20,   Func. Count:    338,   Neg. LLF: 6968.712590478997\n",
            "Iteration:     21,   Func. Count:    353,   Neg. LLF: 6968.704767674649\n",
            "Iteration:     22,   Func. Count:    368,   Neg. LLF: 6968.702793595942\n",
            "Iteration:     23,   Func. Count:    383,   Neg. LLF: 6968.701962541123\n",
            "Iteration:     24,   Func. Count:    398,   Neg. LLF: 6968.701877506195\n",
            "Iteration:     25,   Func. Count:    413,   Neg. LLF: 6968.701872908743\n",
            "Iteration:     26,   Func. Count:    428,   Neg. LLF: 6968.701870850749\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6968.701870850518\n",
            "            Iterations: 26\n",
            "            Function evaluations: 428\n",
            "            Gradient evaluations: 26\n",
            "Iteration:      1,   Func. Count:     10,   Neg. LLF: 7018.610501738858\n",
            "Iteration:      2,   Func. Count:     25,   Neg. LLF: 7002.975824808174\n",
            "Iteration:      3,   Func. Count:     39,   Neg. LLF: 7001.434814294977\n",
            "Iteration:      4,   Func. Count:     51,   Neg. LLF: 6994.417903898426\n",
            "Iteration:      5,   Func. Count:     64,   Neg. LLF: 6989.5917369213785\n",
            "Iteration:      6,   Func. Count:     77,   Neg. LLF: 6989.290001767386\n",
            "Iteration:      7,   Func. Count:     89,   Neg. LLF: 6983.88368603226\n",
            "Iteration:      8,   Func. Count:    102,   Neg. LLF: 6982.6112970738795\n",
            "Iteration:      9,   Func. Count:    113,   Neg. LLF: 6979.137789579865\n",
            "Iteration:     10,   Func. Count:    125,   Neg. LLF: 6978.553459777651\n",
            "Iteration:     11,   Func. Count:    136,   Neg. LLF: 6975.432639763036\n",
            "Iteration:     12,   Func. Count:    147,   Neg. LLF: 6974.327711633423\n",
            "Iteration:     13,   Func. Count:    157,   Neg. LLF: 6973.71009082242\n",
            "Iteration:     14,   Func. Count:    167,   Neg. LLF: 6973.61106774845\n",
            "Iteration:     15,   Func. Count:    177,   Neg. LLF: 6973.609430806267\n",
            "Iteration:     16,   Func. Count:    187,   Neg. LLF: 6973.609318147379\n",
            "Iteration:     17,   Func. Count:    197,   Neg. LLF: 6973.609313810002\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6973.609313808016\n",
            "            Iterations: 17\n",
            "            Function evaluations: 197\n",
            "            Gradient evaluations: 17\n",
            "Iteration:      1,   Func. Count:     11,   Neg. LLF: 7020.851859838598\n",
            "Iteration:      2,   Func. Count:     28,   Neg. LLF: 7001.221078758998\n",
            "Iteration:      3,   Func. Count:     43,   Neg. LLF: 6998.8119390600805\n",
            "Iteration:      4,   Func. Count:     59,   Neg. LLF: 6998.806950277644\n",
            "Iteration:      5,   Func. Count:     74,   Neg. LLF: 6998.776965016392\n",
            "Iteration:      6,   Func. Count:     87,   Neg. LLF: 6998.1043438911065\n",
            "Iteration:      7,   Func. Count:     99,   Neg. LLF: 6991.254661813911\n",
            "Iteration:      8,   Func. Count:    113,   Neg. LLF: 6991.172049201532\n",
            "Iteration:      9,   Func. Count:    124,   Neg. LLF: 6984.058823809628\n",
            "Iteration:     10,   Func. Count:    136,   Neg. LLF: 6980.164280368097\n",
            "Iteration:     11,   Func. Count:    148,   Neg. LLF: 6977.201129611731\n",
            "Iteration:     12,   Func. Count:    161,   Neg. LLF: 6976.816520960259\n",
            "Iteration:     13,   Func. Count:    173,   Neg. LLF: 6976.476014358474\n",
            "Iteration:     14,   Func. Count:    184,   Neg. LLF: 6974.359504626646\n",
            "Iteration:     15,   Func. Count:    195,   Neg. LLF: 6973.6496186546665\n",
            "Iteration:     16,   Func. Count:    206,   Neg. LLF: 6973.6113661662675\n",
            "Iteration:     17,   Func. Count:    217,   Neg. LLF: 6973.609423897253\n",
            "Iteration:     18,   Func. Count:    228,   Neg. LLF: 6973.609314325019\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6973.609313950609\n",
            "            Iterations: 18\n",
            "            Function evaluations: 228\n",
            "            Gradient evaluations: 18\n",
            "Iteration:      1,   Func. Count:     12,   Neg. LLF: 7027.347321088615\n",
            "Iteration:      2,   Func. Count:     30,   Neg. LLF: 7009.56344108246\n",
            "Iteration:      3,   Func. Count:     46,   Neg. LLF: 7008.294770298769\n",
            "Iteration:      4,   Func. Count:     62,   Neg. LLF: 7008.229407121546\n",
            "Iteration:      5,   Func. Count:     77,   Neg. LLF: 7008.169775542016\n",
            "Iteration:      6,   Func. Count:     91,   Neg. LLF: 7007.34429514658\n",
            "Iteration:      7,   Func. Count:    104,   Neg. LLF: 7000.156800781113\n",
            "Iteration:      8,   Func. Count:    119,   Neg. LLF: 6999.986200329766\n",
            "Iteration:      9,   Func. Count:    132,   Neg. LLF: 6992.251053927774\n",
            "Iteration:     10,   Func. Count:    145,   Neg. LLF: 6989.587568886025\n",
            "Iteration:     11,   Func. Count:    158,   Neg. LLF: 6986.33541827695\n",
            "Iteration:     12,   Func. Count:    172,   Neg. LLF: 6985.810787018614\n",
            "Iteration:     13,   Func. Count:    184,   Neg. LLF: 6974.095945830373\n",
            "Iteration:     14,   Func. Count:    196,   Neg. LLF: 6973.835834230622\n",
            "Iteration:     15,   Func. Count:    208,   Neg. LLF: 6973.613326698632\n",
            "Iteration:     16,   Func. Count:    220,   Neg. LLF: 6973.611451978286\n",
            "Iteration:     17,   Func. Count:    232,   Neg. LLF: 6973.6105289673615\n",
            "Iteration:     18,   Func. Count:    244,   Neg. LLF: 6973.609452620314\n",
            "Iteration:     19,   Func. Count:    256,   Neg. LLF: 6973.6093221076735\n",
            "Iteration:     20,   Func. Count:    268,   Neg. LLF: 6973.609314531581\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6973.609313995743\n",
            "            Iterations: 20\n",
            "            Function evaluations: 268\n",
            "            Gradient evaluations: 20\n",
            "Iteration:      1,   Func. Count:     13,   Neg. LLF: 7043.227848455852\n",
            "Iteration:      2,   Func. Count:     32,   Neg. LLF: 7027.1808620057955\n",
            "Iteration:      3,   Func. Count:     49,   Neg. LLF: 7025.708844134959\n",
            "Iteration:      4,   Func. Count:     66,   Neg. LLF: 7025.641834435727\n",
            "Iteration:      5,   Func. Count:     81,   Neg. LLF: 7025.0647116247055\n",
            "Iteration:      6,   Func. Count:     95,   Neg. LLF: 7016.267072020525\n",
            "Iteration:      7,   Func. Count:    110,   Neg. LLF: 7014.18843364848\n",
            "Iteration:      8,   Func. Count:    125,   Neg. LLF: 7013.117782480411\n",
            "Iteration:      9,   Func. Count:    140,   Neg. LLF: 7012.426165071119\n",
            "Iteration:     10,   Func. Count:    154,   Neg. LLF: 6994.093061386366\n",
            "Iteration:     11,   Func. Count:    169,   Neg. LLF: 6993.558404096351\n",
            "Iteration:     12,   Func. Count:    183,   Neg. LLF: 6992.998608569738\n",
            "Iteration:     13,   Func. Count:    196,   Neg. LLF: 6985.55975451986\n",
            "Iteration:     14,   Func. Count:    209,   Neg. LLF: 6976.794903413303\n",
            "Iteration:     15,   Func. Count:    223,   Neg. LLF: 6975.5043785393\n",
            "Iteration:     16,   Func. Count:    236,   Neg. LLF: 6973.874634943608\n",
            "Iteration:     17,   Func. Count:    249,   Neg. LLF: 6973.639317589783\n",
            "Iteration:     18,   Func. Count:    262,   Neg. LLF: 6973.610839765051\n",
            "Iteration:     19,   Func. Count:    275,   Neg. LLF: 6973.609464110679\n",
            "Iteration:     20,   Func. Count:    288,   Neg. LLF: 6973.609322789556\n",
            "Iteration:     21,   Func. Count:    301,   Neg. LLF: 6973.609314747678\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6973.609314031844\n",
            "            Iterations: 21\n",
            "            Function evaluations: 301\n",
            "            Gradient evaluations: 21\n",
            "Iteration:      1,   Func. Count:     11,   Neg. LLF: 7002.5127497699405\n",
            "Iteration:      2,   Func. Count:     28,   Neg. LLF: 6982.162995043133\n",
            "Iteration:      3,   Func. Count:     44,   Neg. LLF: 6977.775099974402\n",
            "Iteration:      4,   Func. Count:     59,   Neg. LLF: 6977.262785871795\n",
            "Iteration:      5,   Func. Count:     73,   Neg. LLF: 6977.188872665493\n",
            "Iteration:      6,   Func. Count:     85,   Neg. LLF: 6973.462472358204\n",
            "Iteration:      7,   Func. Count:     98,   Neg. LLF: 6972.155829708258\n",
            "Iteration:      8,   Func. Count:    113,   Neg. LLF: 6971.889162739348\n",
            "Iteration:      9,   Func. Count:    125,   Neg. LLF: 6969.224195737058\n",
            "Iteration:     10,   Func. Count:    138,   Neg. LLF: 6969.008365547511\n",
            "Iteration:     11,   Func. Count:    150,   Neg. LLF: 6968.559210594903\n",
            "Iteration:     12,   Func. Count:    163,   Neg. LLF: 6967.918371789046\n",
            "Iteration:     13,   Func. Count:    176,   Neg. LLF: 6967.816526479028\n",
            "Iteration:     14,   Func. Count:    189,   Neg. LLF: 6967.780736964192\n",
            "Iteration:     15,   Func. Count:    200,   Neg. LLF: 6967.747744785629\n",
            "Iteration:     16,   Func. Count:    212,   Neg. LLF: 6967.732119514544\n",
            "Iteration:     17,   Func. Count:    224,   Neg. LLF: 6967.722908216636\n",
            "Iteration:     18,   Func. Count:    235,   Neg. LLF: 6967.722903507993\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6967.722903511161\n",
            "            Iterations: 18\n",
            "            Function evaluations: 235\n",
            "            Gradient evaluations: 18\n",
            "Iteration:      1,   Func. Count:     12,   Neg. LLF: 6988.087542466911\n",
            "Iteration:      2,   Func. Count:     30,   Neg. LLF: 6969.358366287802\n",
            "Iteration:      3,   Func. Count:     46,   Neg. LLF: 6968.068998483201\n",
            "Iteration:      4,   Func. Count:     61,   Neg. LLF: 6967.839193711193\n",
            "Iteration:      5,   Func. Count:     76,   Neg. LLF: 6967.673052060971\n",
            "Iteration:      6,   Func. Count:     90,   Neg. LLF: 6967.482702687801\n",
            "Iteration:      7,   Func. Count:    105,   Neg. LLF: 6967.443143313605\n",
            "Iteration:      8,   Func. Count:    119,   Neg. LLF: 6967.282713282093\n",
            "Iteration:      9,   Func. Count:    133,   Neg. LLF: 6967.165963617786\n",
            "Iteration:     10,   Func. Count:    146,   Neg. LLF: 6966.6094528791\n",
            "Iteration:     11,   Func. Count:    160,   Neg. LLF: 6966.576509067985\n",
            "Iteration:     12,   Func. Count:    173,   Neg. LLF: 6966.560012059228\n",
            "Iteration:     13,   Func. Count:    186,   Neg. LLF: 6966.5564915464465\n",
            "Iteration:     14,   Func. Count:    198,   Neg. LLF: 6966.555320875439\n",
            "Iteration:     15,   Func. Count:    210,   Neg. LLF: 6966.55504023304\n",
            "Iteration:     16,   Func. Count:    222,   Neg. LLF: 6966.555037286113\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6966.55503728637\n",
            "            Iterations: 16\n",
            "            Function evaluations: 222\n",
            "            Gradient evaluations: 16\n",
            "Iteration:      1,   Func. Count:     13,   Neg. LLF: 6991.653995683876\n",
            "Iteration:      2,   Func. Count:     31,   Neg. LLF: 6975.10883467068\n",
            "Iteration:      3,   Func. Count:     48,   Neg. LLF: 6973.768027447037\n",
            "Iteration:      4,   Func. Count:     64,   Neg. LLF: 6973.49253171599\n",
            "Iteration:      5,   Func. Count:     80,   Neg. LLF: 6973.000566719662\n",
            "Iteration:      6,   Func. Count:     96,   Neg. LLF: 6972.864184800431\n",
            "Iteration:      7,   Func. Count:    111,   Neg. LLF: 6970.390936117419\n",
            "Iteration:      8,   Func. Count:    127,   Neg. LLF: 6970.301776183762\n",
            "Iteration:      9,   Func. Count:    142,   Neg. LLF: 6970.180802137503\n",
            "Iteration:     10,   Func. Count:    156,   Neg. LLF: 6969.538207721471\n",
            "Iteration:     11,   Func. Count:    170,   Neg. LLF: 6969.05499626569\n",
            "Iteration:     12,   Func. Count:    184,   Neg. LLF: 6968.520650299369\n",
            "Iteration:     13,   Func. Count:    198,   Neg. LLF: 6967.9553362882125\n",
            "Iteration:     14,   Func. Count:    212,   Neg. LLF: 6967.587709410884\n",
            "Iteration:     15,   Func. Count:    225,   Neg. LLF: 6966.642235828136\n",
            "Iteration:     16,   Func. Count:    239,   Neg. LLF: 6966.569980646623\n",
            "Iteration:     17,   Func. Count:    252,   Neg. LLF: 6966.559011331556\n",
            "Iteration:     18,   Func. Count:    265,   Neg. LLF: 6966.55517706357\n",
            "Iteration:     19,   Func. Count:    278,   Neg. LLF: 6966.555050554359\n",
            "Iteration:     20,   Func. Count:    291,   Neg. LLF: 6966.55503753265\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6966.555037430659\n",
            "            Iterations: 20\n",
            "            Function evaluations: 291\n",
            "            Gradient evaluations: 20\n",
            "Iteration:      1,   Func. Count:     14,   Neg. LLF: 7001.480487999619\n",
            "Iteration:      2,   Func. Count:     33,   Neg. LLF: 6985.559379638522\n",
            "Iteration:      3,   Func. Count:     51,   Neg. LLF: 6984.339068493048\n",
            "Iteration:      4,   Func. Count:     68,   Neg. LLF: 6984.101427647264\n",
            "Iteration:      5,   Func. Count:     85,   Neg. LLF: 6983.516991272924\n",
            "Iteration:      6,   Func. Count:    102,   Neg. LLF: 6983.353436269837\n",
            "Iteration:      7,   Func. Count:    117,   Neg. LLF: 6979.286322308004\n",
            "Iteration:      8,   Func. Count:    134,   Neg. LLF: 6979.1269738063165\n",
            "Iteration:      9,   Func. Count:    150,   Neg. LLF: 6978.287366355478\n",
            "Iteration:     10,   Func. Count:    165,   Neg. LLF: 6974.902031143967\n",
            "Iteration:     11,   Func. Count:    180,   Neg. LLF: 6973.150802440293\n",
            "Iteration:     12,   Func. Count:    195,   Neg. LLF: 6972.1462541076835\n",
            "Iteration:     13,   Func. Count:    210,   Neg. LLF: 6968.732758680384\n",
            "Iteration:     14,   Func. Count:    225,   Neg. LLF: 6967.602364140757\n",
            "Iteration:     15,   Func. Count:    240,   Neg. LLF: 6967.234743814026\n",
            "Iteration:     16,   Func. Count:    255,   Neg. LLF: 6966.993714892069\n",
            "Iteration:     17,   Func. Count:    269,   Neg. LLF: 6966.573921595182\n",
            "Iteration:     18,   Func. Count:    283,   Neg. LLF: 6966.556348797205\n",
            "Iteration:     19,   Func. Count:    297,   Neg. LLF: 6966.555143640566\n",
            "Iteration:     20,   Func. Count:    311,   Neg. LLF: 6966.5550863399285\n",
            "Iteration:     21,   Func. Count:    325,   Neg. LLF: 6966.55503723234\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6966.555037187296\n",
            "            Iterations: 21\n",
            "            Function evaluations: 325\n",
            "            Gradient evaluations: 21\n",
            "Iteration:      1,   Func. Count:     12,   Neg. LLF: 7001.315207283811\n",
            "Iteration:      2,   Func. Count:     30,   Neg. LLF: 6980.852637370322\n",
            "Iteration:      3,   Func. Count:     46,   Neg. LLF: 6979.202285113757\n",
            "Iteration:      4,   Func. Count:     62,   Neg. LLF: 6978.840477214064\n",
            "Iteration:      5,   Func. Count:     77,   Neg. LLF: 6978.76854522807\n",
            "Iteration:      6,   Func. Count:     92,   Neg. LLF: 6978.704823290678\n",
            "Iteration:      7,   Func. Count:    107,   Neg. LLF: 6978.640452144564\n",
            "Iteration:      8,   Func. Count:    121,   Neg. LLF: 6978.16455529649\n",
            "Iteration:      9,   Func. Count:    135,   Neg. LLF: 6977.165264329975\n",
            "Iteration:     10,   Func. Count:    148,   Neg. LLF: 6975.109112784212\n",
            "Iteration:     11,   Func. Count:    161,   Neg. LLF: 6972.376134049279\n",
            "Iteration:     12,   Func. Count:    174,   Neg. LLF: 6971.751389060418\n",
            "Iteration:     13,   Func. Count:    187,   Neg. LLF: 6971.404964014344\n",
            "Iteration:     14,   Func. Count:    199,   Neg. LLF: 6968.246510154973\n",
            "Iteration:     15,   Func. Count:    211,   Neg. LLF: 6967.76838805517\n",
            "Iteration:     16,   Func. Count:    223,   Neg. LLF: 6967.752707996514\n",
            "Iteration:     17,   Func. Count:    236,   Neg. LLF: 6967.727511301076\n",
            "Iteration:     18,   Func. Count:    248,   Neg. LLF: 6967.723721067532\n",
            "Iteration:     19,   Func. Count:    260,   Neg. LLF: 6967.722908602807\n",
            "Iteration:     20,   Func. Count:    272,   Neg. LLF: 6967.722903997755\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6967.722903175124\n",
            "            Iterations: 20\n",
            "            Function evaluations: 273\n",
            "            Gradient evaluations: 20\n",
            "Iteration:      1,   Func. Count:     13,   Neg. LLF: 6994.7434277382345\n",
            "Iteration:      2,   Func. Count:     31,   Neg. LLF: 6978.931584725549\n",
            "Iteration:      3,   Func. Count:     48,   Neg. LLF: 6977.793326647056\n",
            "Iteration:      4,   Func. Count:     64,   Neg. LLF: 6977.203717367614\n",
            "Iteration:      5,   Func. Count:     80,   Neg. LLF: 6977.083495159415\n",
            "Iteration:      6,   Func. Count:     95,   Neg. LLF: 6973.838408177855\n",
            "Iteration:      7,   Func. Count:    110,   Neg. LLF: 6972.394587612998\n",
            "Iteration:      8,   Func. Count:    126,   Neg. LLF: 6971.877488963675\n",
            "Iteration:      9,   Func. Count:    141,   Neg. LLF: 6971.62183146461\n",
            "Iteration:     10,   Func. Count:    156,   Neg. LLF: 6971.116169200968\n",
            "Iteration:     11,   Func. Count:    171,   Neg. LLF: 6970.744507429994\n",
            "Iteration:     12,   Func. Count:    185,   Neg. LLF: 6969.721974322736\n",
            "Iteration:     13,   Func. Count:    199,   Neg. LLF: 6967.913407268034\n",
            "Iteration:     14,   Func. Count:    213,   Neg. LLF: 6967.2845405579665\n",
            "Iteration:     15,   Func. Count:    227,   Neg. LLF: 6966.7086162318865\n",
            "Iteration:     16,   Func. Count:    241,   Neg. LLF: 6966.423281802974\n",
            "Iteration:     17,   Func. Count:    255,   Neg. LLF: 6966.284488496278\n",
            "Iteration:     18,   Func. Count:    269,   Neg. LLF: 6966.218835193882\n",
            "Iteration:     19,   Func. Count:    283,   Neg. LLF: 6966.159606670653\n",
            "Iteration:     20,   Func. Count:    297,   Neg. LLF: 6966.132848108968\n",
            "Iteration:     21,   Func. Count:    311,   Neg. LLF: 6966.126021295902\n",
            "Iteration:     22,   Func. Count:    324,   Neg. LLF: 6966.125059232886\n",
            "Iteration:     23,   Func. Count:    337,   Neg. LLF: 6966.124596846392\n",
            "Iteration:     24,   Func. Count:    350,   Neg. LLF: 6966.12457992945\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6966.1245791733545\n",
            "            Iterations: 24\n",
            "            Function evaluations: 351\n",
            "            Gradient evaluations: 24\n",
            "Iteration:      1,   Func. Count:     14,   Neg. LLF: 6998.289185640811\n",
            "Iteration:      2,   Func. Count:     33,   Neg. LLF: 6983.078371828833\n",
            "Iteration:      3,   Func. Count:     51,   Neg. LLF: 6981.869544345513\n",
            "Iteration:      4,   Func. Count:     68,   Neg. LLF: 6981.00302702293\n",
            "Iteration:      5,   Func. Count:     85,   Neg. LLF: 6980.447953903686\n",
            "Iteration:      6,   Func. Count:    100,   Neg. LLF: 6972.7360745700935\n",
            "Iteration:      7,   Func. Count:    117,   Neg. LLF: 6972.556795348832\n",
            "Iteration:      8,   Func. Count:    133,   Neg. LLF: 6972.013671174074\n",
            "Iteration:      9,   Func. Count:    149,   Neg. LLF: 6971.020490449526\n",
            "Iteration:     10,   Func. Count:    165,   Neg. LLF: 6970.284543489796\n",
            "Iteration:     11,   Func. Count:    180,   Neg. LLF: 6968.425349404752\n",
            "Iteration:     12,   Func. Count:    195,   Neg. LLF: 6968.230138530512\n",
            "Iteration:     13,   Func. Count:    210,   Neg. LLF: 6967.611196432368\n",
            "Iteration:     14,   Func. Count:    225,   Neg. LLF: 6967.148709161044\n",
            "Iteration:     15,   Func. Count:    240,   Neg. LLF: 6966.6023555346\n",
            "Iteration:     16,   Func. Count:    255,   Neg. LLF: 6966.33318953163\n",
            "Iteration:     17,   Func. Count:    270,   Neg. LLF: 6966.206685437002\n",
            "Iteration:     18,   Func. Count:    286,   Neg. LLF: 6966.195296084965\n",
            "Iteration:     19,   Func. Count:    301,   Neg. LLF: 6966.1375080403905\n",
            "Iteration:     20,   Func. Count:    315,   Neg. LLF: 6966.131846926822\n",
            "Iteration:     21,   Func. Count:    330,   Neg. LLF: 6966.1265308542725\n",
            "Iteration:     22,   Func. Count:    345,   Neg. LLF: 6966.125376906111\n",
            "Iteration:     23,   Func. Count:    359,   Neg. LLF: 6966.12487033553\n",
            "Iteration:     24,   Func. Count:    373,   Neg. LLF: 6966.1243726000475\n",
            "Iteration:     25,   Func. Count:    387,   Neg. LLF: 6966.124279413894\n",
            "Iteration:     26,   Func. Count:    401,   Neg. LLF: 6966.124273338676\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6966.124273338723\n",
            "            Iterations: 26\n",
            "            Function evaluations: 401\n",
            "            Gradient evaluations: 26\n",
            "Iteration:      1,   Func. Count:     15,   Neg. LLF: 7007.344476075366\n",
            "Iteration:      2,   Func. Count:     35,   Neg. LLF: 6992.321989474403\n",
            "Iteration:      3,   Func. Count:     54,   Neg. LLF: 6991.197172591343\n",
            "Iteration:      4,   Func. Count:     71,   Neg. LLF: 6990.6937125306285\n",
            "Iteration:      5,   Func. Count:     88,   Neg. LLF: 6981.748923878558\n",
            "Iteration:      6,   Func. Count:    106,   Neg. LLF: 6981.327676712135\n",
            "Iteration:      7,   Func. Count:    123,   Neg. LLF: 6977.705579429902\n",
            "Iteration:      8,   Func. Count:    141,   Neg. LLF: 6976.345267420511\n",
            "Iteration:      9,   Func. Count:    158,   Neg. LLF: 6973.828676389911\n",
            "Iteration:     10,   Func. Count:    175,   Neg. LLF: 6971.349866980311\n",
            "Iteration:     11,   Func. Count:    192,   Neg. LLF: 6970.948005234052\n",
            "Iteration:     12,   Func. Count:    208,   Neg. LLF: 6968.5181925161105\n",
            "Iteration:     13,   Func. Count:    225,   Neg. LLF: 6968.202623124302\n",
            "Iteration:     14,   Func. Count:    241,   Neg. LLF: 6967.712137528357\n",
            "Iteration:     15,   Func. Count:    258,   Neg. LLF: 6967.510849690425\n",
            "Iteration:     16,   Func. Count:    274,   Neg. LLF: 6967.056536034195\n",
            "Iteration:     17,   Func. Count:    290,   Neg. LLF: 6966.57912639261\n",
            "Iteration:     18,   Func. Count:    306,   Neg. LLF: 6966.322448140507\n",
            "Iteration:     19,   Func. Count:    322,   Neg. LLF: 6966.1769185175\n",
            "Iteration:     20,   Func. Count:    337,   Neg. LLF: 6966.151574705351\n",
            "Iteration:     21,   Func. Count:    353,   Neg. LLF: 6966.123478223184\n",
            "Iteration:     22,   Func. Count:    368,   Neg. LLF: 6966.110097573095\n",
            "Iteration:     23,   Func. Count:    383,   Neg. LLF: 6966.109172017403\n",
            "Iteration:     24,   Func. Count:    398,   Neg. LLF: 6966.109144435107\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6966.109143807642\n",
            "            Iterations: 24\n",
            "            Function evaluations: 399\n",
            "            Gradient evaluations: 24\n",
            "Iteration:      1,   Func. Count:     13,   Neg. LLF: 7005.185366256686\n",
            "Iteration:      2,   Func. Count:     32,   Neg. LLF: 6985.269167260192\n",
            "Iteration:      3,   Func. Count:     49,   Neg. LLF: 6982.346049414447\n",
            "Iteration:      4,   Func. Count:     66,   Neg. LLF: 6982.156906942155\n",
            "Iteration:      5,   Func. Count:     81,   Neg. LLF: 6981.162589570709\n",
            "Iteration:      6,   Func. Count:     96,   Neg. LLF: 6978.4627204286635\n",
            "Iteration:      7,   Func. Count:    113,   Neg. LLF: 6978.4142409238775\n",
            "Iteration:      8,   Func. Count:    129,   Neg. LLF: 6978.348133853263\n",
            "Iteration:      9,   Func. Count:    144,   Neg. LLF: 6978.27381702947\n",
            "Iteration:     10,   Func. Count:    158,   Neg. LLF: 6976.5787228281215\n",
            "Iteration:     11,   Func. Count:    172,   Neg. LLF: 6971.6431883167825\n",
            "Iteration:     12,   Func. Count:    186,   Neg. LLF: 6970.326361702544\n",
            "Iteration:     13,   Func. Count:    200,   Neg. LLF: 6969.605513534857\n",
            "Iteration:     14,   Func. Count:    213,   Neg. LLF: 6967.958108307462\n",
            "Iteration:     15,   Func. Count:    226,   Neg. LLF: 6967.791703474131\n",
            "Iteration:     16,   Func. Count:    239,   Neg. LLF: 6967.733912316979\n",
            "Iteration:     17,   Func. Count:    252,   Neg. LLF: 6967.725386625101\n",
            "Iteration:     18,   Func. Count:    265,   Neg. LLF: 6967.722967686639\n",
            "Iteration:     19,   Func. Count:    278,   Neg. LLF: 6967.72291334516\n",
            "Iteration:     20,   Func. Count:    291,   Neg. LLF: 6967.722904755701\n",
            "Iteration:     21,   Func. Count:    304,   Neg. LLF: 6967.722903497316\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6967.722903497932\n",
            "            Iterations: 21\n",
            "            Function evaluations: 304\n",
            "            Gradient evaluations: 21\n",
            "Iteration:      1,   Func. Count:     14,   Neg. LLF: 7001.010122220114\n",
            "Iteration:      2,   Func. Count:     33,   Neg. LLF: 6984.667497696582\n",
            "Iteration:      3,   Func. Count:     51,   Neg. LLF: 6983.77615298264\n",
            "Iteration:      4,   Func. Count:     67,   Neg. LLF: 6979.774604886187\n",
            "Iteration:      5,   Func. Count:     83,   Neg. LLF: 6978.210103429385\n",
            "Iteration:      6,   Func. Count:     99,   Neg. LLF: 6977.743797898802\n",
            "Iteration:      7,   Func. Count:    115,   Neg. LLF: 6973.079230829739\n",
            "Iteration:      8,   Func. Count:    133,   Neg. LLF: 6972.890126457472\n",
            "Iteration:      9,   Func. Count:    149,   Neg. LLF: 6971.958525735248\n",
            "Iteration:     10,   Func. Count:    165,   Neg. LLF: 6971.090341708574\n",
            "Iteration:     11,   Func. Count:    180,   Neg. LLF: 6969.442584868371\n",
            "Iteration:     12,   Func. Count:    195,   Neg. LLF: 6969.019850342507\n",
            "Iteration:     13,   Func. Count:    210,   Neg. LLF: 6967.4274218779865\n",
            "Iteration:     14,   Func. Count:    225,   Neg. LLF: 6967.1543312220165\n",
            "Iteration:     15,   Func. Count:    240,   Neg. LLF: 6966.616230920895\n",
            "Iteration:     16,   Func. Count:    254,   Neg. LLF: 6966.510921732476\n",
            "Iteration:     17,   Func. Count:    269,   Neg. LLF: 6966.239604672333\n",
            "Iteration:     18,   Func. Count:    285,   Neg. LLF: 6966.1929327531725\n",
            "Iteration:     19,   Func. Count:    301,   Neg. LLF: 6966.189473641356\n",
            "Iteration:     20,   Func. Count:    316,   Neg. LLF: 6966.139798710891\n",
            "Iteration:     21,   Func. Count:    330,   Neg. LLF: 6966.12743439264\n",
            "Iteration:     22,   Func. Count:    344,   Neg. LLF: 6966.124644729847\n",
            "Iteration:     23,   Func. Count:    358,   Neg. LLF: 6966.12459376781\n",
            "Iteration:     24,   Func. Count:    372,   Neg. LLF: 6966.124580893638\n",
            "Iteration:     25,   Func. Count:    386,   Neg. LLF: 6966.124579245648\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6966.1245792453\n",
            "            Iterations: 25\n",
            "            Function evaluations: 386\n",
            "            Gradient evaluations: 25\n",
            "Iteration:      1,   Func. Count:     15,   Neg. LLF: 7005.747821716197\n",
            "Iteration:      2,   Func. Count:     35,   Neg. LLF: 6990.455019709589\n",
            "Iteration:      3,   Func. Count:     54,   Neg. LLF: 6989.380757046642\n",
            "Iteration:      4,   Func. Count:     71,   Neg. LLF: 6987.225058022224\n",
            "Iteration:      5,   Func. Count:     88,   Neg. LLF: 6980.165407347333\n",
            "Iteration:      6,   Func. Count:    105,   Neg. LLF: 6974.464810358107\n",
            "Iteration:      7,   Func. Count:    124,   Neg. LLF: 6974.072671835591\n",
            "Iteration:      8,   Func. Count:    141,   Neg. LLF: 6973.32532166526\n",
            "Iteration:      9,   Func. Count:    158,   Neg. LLF: 6968.907966438118\n",
            "Iteration:     10,   Func. Count:    175,   Neg. LLF: 6967.605200352122\n",
            "Iteration:     11,   Func. Count:    191,   Neg. LLF: 6967.34498209001\n",
            "Iteration:     12,   Func. Count:    208,   Neg. LLF: 6967.239346899549\n",
            "Iteration:     13,   Func. Count:    225,   Neg. LLF: 6967.123822041438\n",
            "Iteration:     14,   Func. Count:    242,   Neg. LLF: 6966.9428543607955\n",
            "Iteration:     15,   Func. Count:    258,   Neg. LLF: 6966.86158423359\n",
            "Iteration:     16,   Func. Count:    275,   Neg. LLF: 6966.716201780187\n",
            "Iteration:     17,   Func. Count:    290,   Neg. LLF: 6966.141212263329\n",
            "Iteration:     18,   Func. Count:    305,   Neg. LLF: 6966.022027832488\n",
            "Iteration:     19,   Func. Count:    320,   Neg. LLF: 6965.982016204209\n",
            "Iteration:     20,   Func. Count:    335,   Neg. LLF: 6965.961442243622\n",
            "Iteration:     21,   Func. Count:    350,   Neg. LLF: 6965.949551675782\n",
            "Iteration:     22,   Func. Count:    365,   Neg. LLF: 6965.945313315285\n",
            "Iteration:     23,   Func. Count:    380,   Neg. LLF: 6965.943401190596\n",
            "Iteration:     24,   Func. Count:    395,   Neg. LLF: 6965.943231140972\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6965.9432303856265\n",
            "            Iterations: 24\n",
            "            Function evaluations: 396\n",
            "            Gradient evaluations: 24\n",
            "Iteration:      1,   Func. Count:     16,   Neg. LLF: 7012.8915809189075\n",
            "Iteration:      2,   Func. Count:     37,   Neg. LLF: 6998.061222379321\n",
            "Iteration:      3,   Func. Count:     57,   Neg. LLF: 6997.028385527017\n",
            "Iteration:      4,   Func. Count:     75,   Neg. LLF: 6993.900706772015\n",
            "Iteration:      5,   Func. Count:     93,   Neg. LLF: 6981.381853516816\n",
            "Iteration:      6,   Func. Count:    112,   Neg. LLF: 6980.77248008055\n",
            "Iteration:      7,   Func. Count:    130,   Neg. LLF: 6974.108859853584\n",
            "Iteration:      8,   Func. Count:    149,   Neg. LLF: 6972.657236480436\n",
            "Iteration:      9,   Func. Count:    167,   Neg. LLF: 6969.736747467968\n",
            "Iteration:     10,   Func. Count:    185,   Neg. LLF: 6966.973750871535\n",
            "Iteration:     11,   Func. Count:    203,   Neg. LLF: 6966.4265406490495\n",
            "Iteration:     12,   Func. Count:    221,   Neg. LLF: 6966.2195232909535\n",
            "Iteration:     13,   Func. Count:    239,   Neg. LLF: 6966.120844169545\n",
            "Iteration:     14,   Func. Count:    257,   Neg. LLF: 6966.063325702713\n",
            "Iteration:     15,   Func. Count:    274,   Neg. LLF: 6965.837342697685\n",
            "Iteration:     16,   Func. Count:    291,   Neg. LLF: 6965.7780248015115\n",
            "Iteration:     17,   Func. Count:    308,   Neg. LLF: 6965.692556378555\n",
            "Iteration:     18,   Func. Count:    325,   Neg. LLF: 6965.662253003455\n",
            "Iteration:     19,   Func. Count:    342,   Neg. LLF: 6965.621216094959\n",
            "Iteration:     20,   Func. Count:    359,   Neg. LLF: 6965.617233589781\n",
            "Iteration:     21,   Func. Count:    375,   Neg. LLF: 6965.602790546733\n",
            "Iteration:     22,   Func. Count:    391,   Neg. LLF: 6965.598866945246\n",
            "Iteration:     23,   Func. Count:    407,   Neg. LLF: 6965.597774241742\n",
            "Iteration:     24,   Func. Count:    423,   Neg. LLF: 6965.597762684769\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6965.597761772378\n",
            "            Iterations: 24\n",
            "            Function evaluations: 424\n",
            "            Gradient evaluations: 24\n",
            "ARIMA-GARCH order is (4, 2, 2)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IHWHbA0X-ih6",
        "colab_type": "text"
      },
      "source": [
        "#### Step Two: FIt the Model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6eMXHX7o-ih7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 374
        },
        "outputId": "24bc5da2-f2a3-40b2-a256-99e27bed0456"
      },
      "source": [
        "model = arch_model(hist_ret, mean='ARX', lags=l, vol='Garch', p=p, o=0, q=q, dist='Normal')\n",
        "res = model.fit(last_obs=split_date)"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iteration:      1,   Func. Count:     12,   Neg. LLF: 6988.087542466911\n",
            "Iteration:      2,   Func. Count:     30,   Neg. LLF: 6969.358366287802\n",
            "Iteration:      3,   Func. Count:     46,   Neg. LLF: 6968.068998483201\n",
            "Iteration:      4,   Func. Count:     61,   Neg. LLF: 6967.839193711193\n",
            "Iteration:      5,   Func. Count:     76,   Neg. LLF: 6967.673052060971\n",
            "Iteration:      6,   Func. Count:     90,   Neg. LLF: 6967.482702687801\n",
            "Iteration:      7,   Func. Count:    105,   Neg. LLF: 6967.443143313605\n",
            "Iteration:      8,   Func. Count:    119,   Neg. LLF: 6967.282713282093\n",
            "Iteration:      9,   Func. Count:    133,   Neg. LLF: 6967.165963617786\n",
            "Iteration:     10,   Func. Count:    146,   Neg. LLF: 6966.6094528791\n",
            "Iteration:     11,   Func. Count:    160,   Neg. LLF: 6966.576509067985\n",
            "Iteration:     12,   Func. Count:    173,   Neg. LLF: 6966.560012059228\n",
            "Iteration:     13,   Func. Count:    186,   Neg. LLF: 6966.5564915464465\n",
            "Iteration:     14,   Func. Count:    198,   Neg. LLF: 6966.555320875439\n",
            "Iteration:     15,   Func. Count:    210,   Neg. LLF: 6966.55504023304\n",
            "Iteration:     16,   Func. Count:    222,   Neg. LLF: 6966.555037286113\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 6966.55503728637\n",
            "            Iterations: 16\n",
            "            Function evaluations: 222\n",
            "            Gradient evaluations: 16\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i9rz7NS5-ih9",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 545
        },
        "outputId": "b59e6389-d513-45ed-e6eb-9c7f23483ea8"
      },
      "source": [
        "res.summary()"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>AR - GARCH Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>        <td>Close</td>       <th>  R-squared:         </th>  <td>   0.009</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Mean Model:</th>            <td>AR</td>         <th>  Adj. R-squared:    </th>  <td>   0.008</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Vol Model:</th>            <td>GARCH</td>       <th>  Log-Likelihood:    </th> <td>  -6966.56</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Distribution:</th>        <td>Normal</td>       <th>  AIC:               </th> <td>   13953.1</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>        <td>Maximum Likelihood</td> <th>  BIC:               </th> <td>   14018.5</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                        <td></td>          <th>  No. Observations:  </th>    <td>5106</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>           <td>Wed, Jul 01 2020</td>  <th>  Df Residuals:      </th>    <td>5096</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>               <td>01:35:19</td>      <th>  Df Model:          </th>     <td>10</td>    \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Mean Model</caption>\n",
              "<tr>\n",
              "      <td></td>        <th>coef</th>      <th>std err</th>      <th>t</th>       <th>P>|t|</th>      <th>95.0% Conf. Int.</th>    \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Const</th>    <td>    0.0711</td>  <td>1.181e-02</td> <td>    6.015</td> <td>1.794e-09</td>  <td>[4.790e-02,9.420e-02]</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Close[1]</th> <td>   -0.0612</td>  <td>1.452e-02</td> <td>   -4.214</td> <td>2.513e-05</td> <td>[-8.963e-02,-3.272e-02]</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Close[2]</th> <td>   -0.0307</td>  <td>1.544e-02</td> <td>   -1.991</td> <td>4.645e-02</td> <td>[-6.100e-02,-4.833e-04]</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Close[3]</th> <td>   -0.0105</td>  <td>1.502e-02</td> <td>   -0.702</td> <td>    0.483</td> <td>[-3.999e-02,1.890e-02]</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Close[4]</th> <td>-8.6654e-03</td> <td>1.547e-02</td> <td>   -0.560</td> <td>    0.575</td> <td>[-3.899e-02,2.166e-02]</td> \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Volatility Model</caption>\n",
              "<tr>\n",
              "      <td></td>        <th>coef</th>     <th>std err</th>      <th>t</th>       <th>P>|t|</th>     <th>95.0% Conf. Int.</th>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>omega</th>    <td>    0.0386</td> <td>1.037e-02</td> <td>    3.720</td> <td>1.993e-04</td> <td>[1.825e-02,5.890e-02]</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>alpha[1]</th> <td>    0.0829</td> <td>2.589e-02</td> <td>    3.204</td> <td>1.357e-03</td>  <td>[3.220e-02,  0.134]</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>alpha[2]</th> <td>    0.1295</td> <td>3.496e-02</td> <td>    3.703</td> <td>2.134e-04</td>  <td>[6.093e-02,  0.198]</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>beta[1]</th>  <td>    0.2733</td> <td>    0.426</td> <td>    0.642</td> <td>    0.521</td>   <td>[ -0.561,  1.108]</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>beta[2]</th>  <td>    0.4874</td> <td>    0.379</td> <td>    1.285</td> <td>    0.199</td>   <td>[ -0.256,  1.231]</td>  \n",
              "</tr>\n",
              "</table><br/><br/>Covariance estimator: robust"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                           AR - GARCH Model Results                           \n",
              "==============================================================================\n",
              "Dep. Variable:                  Close   R-squared:                       0.009\n",
              "Mean Model:                        AR   Adj. R-squared:                  0.008\n",
              "Vol Model:                      GARCH   Log-Likelihood:               -6966.56\n",
              "Distribution:                  Normal   AIC:                           13953.1\n",
              "Method:            Maximum Likelihood   BIC:                           14018.5\n",
              "                                        No. Observations:                 5106\n",
              "Date:                Wed, Jul 01 2020   Df Residuals:                     5096\n",
              "Time:                        01:35:19   Df Model:                           10\n",
              "                                   Mean Model                                  \n",
              "===============================================================================\n",
              "                  coef    std err          t      P>|t|        95.0% Conf. Int.\n",
              "-------------------------------------------------------------------------------\n",
              "Const           0.0711  1.181e-02      6.015  1.794e-09   [4.790e-02,9.420e-02]\n",
              "Close[1]       -0.0612  1.452e-02     -4.214  2.513e-05 [-8.963e-02,-3.272e-02]\n",
              "Close[2]       -0.0307  1.544e-02     -1.991  4.645e-02 [-6.100e-02,-4.833e-04]\n",
              "Close[3]       -0.0105  1.502e-02     -0.702      0.483  [-3.999e-02,1.890e-02]\n",
              "Close[4]   -8.6654e-03  1.547e-02     -0.560      0.575  [-3.899e-02,2.166e-02]\n",
              "                              Volatility Model                              \n",
              "============================================================================\n",
              "                 coef    std err          t      P>|t|      95.0% Conf. Int.\n",
              "----------------------------------------------------------------------------\n",
              "omega          0.0386  1.037e-02      3.720  1.993e-04 [1.825e-02,5.890e-02]\n",
              "alpha[1]       0.0829  2.589e-02      3.204  1.357e-03   [3.220e-02,  0.134]\n",
              "alpha[2]       0.1295  3.496e-02      3.703  2.134e-04   [6.093e-02,  0.198]\n",
              "beta[1]        0.2733      0.426      0.642      0.521     [ -0.561,  1.108]\n",
              "beta[2]        0.4874      0.379      1.285      0.199     [ -0.256,  1.231]\n",
              "============================================================================\n",
              "\n",
              "Covariance estimator: robust\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ot2ZiRQb-iiA",
        "colab_type": "text"
      },
      "source": [
        "#### Step Three: Evaluate Model via Residuals"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q572A91W-iiA",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "3c03e618-1e65-4e25-9389-d62c149d566d"
      },
      "source": [
        "res.plot(annualize='D')\n",
        "std_resid = res.resid / res.conditional_volatility\n",
        "std_resid.dropna(inplace=True)"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mQ2OLOAS-iiE",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "outputId": "e446ff12-0772-4ed9-8c6e-e7c4ded898db"
      },
      "source": [
        "sm.qqplot(std_resid, line='s');"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "x3FIW_UY-iiH",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        },
        "outputId": "343e3d90-bac2-4537-e36c-61ec2bff91d3"
      },
      "source": [
        "stat, p = normaltest(std_resid)\n",
        "print(f'Statistics={stat:.3f}, p={p:.3f}')       # H0: Gaussian\n",
        "stat, p = shapiro(std_resid)\n",
        "print(f'Statistics={stat:.3f}, p={p:.3f}')       # H0: Gaussian"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Statistics=385.475, p=0.000\n",
            "Statistics=0.982, p=0.000\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/scipy/stats/morestats.py:1676: UserWarning: p-value may not be accurate for N > 5000.\n",
            "  warnings.warn(\"p-value may not be accurate for N > 5000.\")\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n2qVoUti-iiJ",
        "colab_type": "text"
      },
      "source": [
        "#### Step Four: Forecast"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "C4NHuBn_-iiJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "forecasts = res.forecast(horizon=1, start=split_date)"
      ],
      "execution_count": 22,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B8AUisNu-iiL",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 320
        },
        "outputId": "29d45884-daa8-4632-9b40-c4f60fce6919"
      },
      "source": [
        "conf = np.sqrt(forecasts.variance[split_date:])*1.96\n",
        "\n",
        "plt.figure(figsize=(12, 5))\n",
        "plt.plot(forecasts.mean[split_date:], label='one step rolling')\n",
        "plt.plot(hist_ret[split_date:], label='actual')\n",
        "plt.fill_between(hist_ret[split_date:].index, (forecasts.mean[split_date:]-conf).values.reshape(-1), (forecasts.mean[split_date:]+conf).values.reshape(-1), color='gray', alpha=0.7)\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LkfIlw2MA-25",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}